Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block

(1) 15 ms(2) 20 ms (3) 25 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 8 ms (8) 10 ms

If m=2 kg px = +4 kgms py = -3 kgmsWhat is the magnitude of the momentum of the block

+4 kgmiddotms

-3 kgmiddotmsmskg 5

)3(4 22

22

p

p

ppp yx

Could also calculate velocity components directly then find magnitude (speed)

px = mmiddotvx py = mmiddotvy

4kgmiddotms = 2kg vx -3kgmiddotms = 2kg vy

vx = 2 ms vy = -15 ms

Find speedp = mv

5 kgms = 2kg vv = 25 ms

ms 52

)51(2 22

22

v

v

vvv yx

F versus t graph

bull Impulse equal to area under F vs t graphbull Vector quantity need to account for directionbull Impulse in x direction will only affect

momentum in xndash will not change momentum in y

pJ XX pJ YY pJ

Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table

1 Ball A 2 Ball B 3 Both feel the same impulse

Greater change in momentum (not only stopped but reversed direction)

mtF

mtF

mmtF

vmvmtF f

10

))5(5(

)5()5(0

Careful with signs VECTORS Suppose initial velocity is -5ms and final velocity is + 5ms (presume +y is up)

A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse

(1) = 90

(2) 45 lt lt 90

(3) = 45

(4) 0 lt lt 45

(5) = 0

After impulse px = 6 kg ms (same as before)

py = 10 kg ms

Greater momentum in y than in x

6 kgmiddotms

10 kgmiddotms

Collisionsbull During collision F12 = - F21 during whole time

bull J12 = J21

bull (Sum ext forces + sum int forces)Δt = pf ndash p0

bull Sum int forces always zero

bull If sum of average external forces = 0

bull Momentum stays same ndash Conservedbull System ndash objectgroup of objects consideringbull Total momentum of system ndash add momenta

from each object

fpp 0

Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system

(1) 11000 kgms to the left(2) 1000 kgms to the left(3) 0 kgms(4) 1000 kgms to the right(5) 11000 kgms to the right

6000 kg ms to right 5000 kg ms to left

After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)

(1) to the left(2) they will be stationary(3) to the right

Collision with momentum conserved pinitial to right pfinal to right

vfinal = 014 ms to the right

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

If m=2 kg px = +4 kgms py = -3 kgmsWhat is the magnitude of the momentum of the block

+4 kgmiddotms

-3 kgmiddotmsmskg 5

)3(4 22

22

p

p

ppp yx

Could also calculate velocity components directly then find magnitude (speed)

px = mmiddotvx py = mmiddotvy

4kgmiddotms = 2kg vx -3kgmiddotms = 2kg vy

vx = 2 ms vy = -15 ms

Find speedp = mv

5 kgms = 2kg vv = 25 ms

ms 52

)51(2 22

22

v

v

vvv yx

F versus t graph

bull Impulse equal to area under F vs t graphbull Vector quantity need to account for directionbull Impulse in x direction will only affect

momentum in xndash will not change momentum in y

pJ XX pJ YY pJ

Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table

1 Ball A 2 Ball B 3 Both feel the same impulse

Greater change in momentum (not only stopped but reversed direction)

mtF

mtF

mmtF

vmvmtF f

10

))5(5(

)5()5(0

Careful with signs VECTORS Suppose initial velocity is -5ms and final velocity is + 5ms (presume +y is up)

A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse

(1) = 90

(2) 45 lt lt 90

(3) = 45

(4) 0 lt lt 45

(5) = 0

After impulse px = 6 kg ms (same as before)

py = 10 kg ms

Greater momentum in y than in x

6 kgmiddotms

10 kgmiddotms

Collisionsbull During collision F12 = - F21 during whole time

bull J12 = J21

bull (Sum ext forces + sum int forces)Δt = pf ndash p0

bull Sum int forces always zero

bull If sum of average external forces = 0

bull Momentum stays same ndash Conservedbull System ndash objectgroup of objects consideringbull Total momentum of system ndash add momenta

from each object

fpp 0

Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system

(1) 11000 kgms to the left(2) 1000 kgms to the left(3) 0 kgms(4) 1000 kgms to the right(5) 11000 kgms to the right

6000 kg ms to right 5000 kg ms to left

After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)

(1) to the left(2) they will be stationary(3) to the right

Collision with momentum conserved pinitial to right pfinal to right

vfinal = 014 ms to the right

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

F versus t graph

bull Impulse equal to area under F vs t graphbull Vector quantity need to account for directionbull Impulse in x direction will only affect

momentum in xndash will not change momentum in y

pJ XX pJ YY pJ

Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table

1 Ball A 2 Ball B 3 Both feel the same impulse

Greater change in momentum (not only stopped but reversed direction)

mtF

mtF

mmtF

vmvmtF f

10

))5(5(

)5()5(0

Careful with signs VECTORS Suppose initial velocity is -5ms and final velocity is + 5ms (presume +y is up)

A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse

(1) = 90

(2) 45 lt lt 90

(3) = 45

(4) 0 lt lt 45

(5) = 0

After impulse px = 6 kg ms (same as before)

py = 10 kg ms

Greater momentum in y than in x

6 kgmiddotms

10 kgmiddotms

Collisionsbull During collision F12 = - F21 during whole time

bull J12 = J21

bull (Sum ext forces + sum int forces)Δt = pf ndash p0

bull Sum int forces always zero

bull If sum of average external forces = 0

bull Momentum stays same ndash Conservedbull System ndash objectgroup of objects consideringbull Total momentum of system ndash add momenta

from each object

fpp 0

Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system

(1) 11000 kgms to the left(2) 1000 kgms to the left(3) 0 kgms(4) 1000 kgms to the right(5) 11000 kgms to the right

6000 kg ms to right 5000 kg ms to left

After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)

(1) to the left(2) they will be stationary(3) to the right

Collision with momentum conserved pinitial to right pfinal to right

vfinal = 014 ms to the right

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table

1 Ball A 2 Ball B 3 Both feel the same impulse

Greater change in momentum (not only stopped but reversed direction)

mtF

mtF

mmtF

vmvmtF f

10

))5(5(

)5()5(0

Careful with signs VECTORS Suppose initial velocity is -5ms and final velocity is + 5ms (presume +y is up)

A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse

(1) = 90

(2) 45 lt lt 90

(3) = 45

(4) 0 lt lt 45

(5) = 0

After impulse px = 6 kg ms (same as before)

py = 10 kg ms

Greater momentum in y than in x

6 kgmiddotms

10 kgmiddotms

Collisionsbull During collision F12 = - F21 during whole time

bull J12 = J21

bull (Sum ext forces + sum int forces)Δt = pf ndash p0

bull Sum int forces always zero

bull If sum of average external forces = 0

bull Momentum stays same ndash Conservedbull System ndash objectgroup of objects consideringbull Total momentum of system ndash add momenta

from each object

fpp 0

Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system

(1) 11000 kgms to the left(2) 1000 kgms to the left(3) 0 kgms(4) 1000 kgms to the right(5) 11000 kgms to the right

6000 kg ms to right 5000 kg ms to left

After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)

(1) to the left(2) they will be stationary(3) to the right

Collision with momentum conserved pinitial to right pfinal to right

vfinal = 014 ms to the right

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse

(1) = 90

(2) 45 lt lt 90

(3) = 45

(4) 0 lt lt 45

(5) = 0

After impulse px = 6 kg ms (same as before)

py = 10 kg ms

Greater momentum in y than in x

6 kgmiddotms

10 kgmiddotms

Collisionsbull During collision F12 = - F21 during whole time

bull J12 = J21

bull (Sum ext forces + sum int forces)Δt = pf ndash p0

bull Sum int forces always zero

bull If sum of average external forces = 0

bull Momentum stays same ndash Conservedbull System ndash objectgroup of objects consideringbull Total momentum of system ndash add momenta

from each object

fpp 0

Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system

(1) 11000 kgms to the left(2) 1000 kgms to the left(3) 0 kgms(4) 1000 kgms to the right(5) 11000 kgms to the right

6000 kg ms to right 5000 kg ms to left

After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)

(1) to the left(2) they will be stationary(3) to the right

Collision with momentum conserved pinitial to right pfinal to right

vfinal = 014 ms to the right

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Collisionsbull During collision F12 = - F21 during whole time

bull J12 = J21

bull (Sum ext forces + sum int forces)Δt = pf ndash p0

bull Sum int forces always zero

bull If sum of average external forces = 0

bull Momentum stays same ndash Conservedbull System ndash objectgroup of objects consideringbull Total momentum of system ndash add momenta

from each object

fpp 0

Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system

(1) 11000 kgms to the left(2) 1000 kgms to the left(3) 0 kgms(4) 1000 kgms to the right(5) 11000 kgms to the right

6000 kg ms to right 5000 kg ms to left

After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)

(1) to the left(2) they will be stationary(3) to the right

Collision with momentum conserved pinitial to right pfinal to right

vfinal = 014 ms to the right

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system

(1) 11000 kgms to the left(2) 1000 kgms to the left(3) 0 kgms(4) 1000 kgms to the right(5) 11000 kgms to the right

6000 kg ms to right 5000 kg ms to left

After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)

(1) to the left(2) they will be stationary(3) to the right

Collision with momentum conserved pinitial to right pfinal to right

vfinal = 014 ms to the right

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)

(1) to the left(2) they will be stationary(3) to the right

Collision with momentum conserved pinitial to right pfinal to right

vfinal = 014 ms to the right

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Two cars collide and stick together How fast will they be traveling after the collision

2ms 3ms

4000kg 2000kg

pinitial = pfinal

p1i + p2i = p12f

m1v1i + m2v2i = (m1+ m2)vf

4000kg2ms + 2000kg(-3ms) = (6000kg)vf

2000kgms =(6000kg) vf

Vf =+033 ms

+x

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest and becomes embedded What is the velocity of the bullet and the block after the event

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

A 1kg bullet has a horizontal velocity of 200 ms It strikes to a wooden block of 10 kg initially at rest If the bullet pass through the block and its final speed is 100 ms what will be the velocity of the bullet

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (3m) v

v = 2 ms

Clicker

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car

(1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms(5) 5 ms (6) 6 ms (7) 12 ms (8) 18 ms (9) 0 ms

pinitial = pfinal

m6 = (2m) 1ms + mv

v = 4 ms

Clicker

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Collisions

bull All collisions conserve momentumbull ELASTIC KE conserves bull INELASTIC KE does not conservebull perfectly inelastic ndash stick together (final v same)

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Elastic Collisions

KE KE01 + KE02 = KEf1 + KEf2

p p01 + p02 = pf1 + pf2

22

21

220

210 2

121

21

21

ff mvmvmvmv

212010 ff mvmvmvmv

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

ExampleA bullet of 01 kg is fired to a wooden block of mass 5 kg hanged by a rope as shown After the bullet hits the block it is embedded in the block If the blockswings (bullet is embedded) to a height of 05 m due to the impact what is the Initial speed of the bullet

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

ClickerA ball is attached to a wire held horizontally and dropped It strikes a block that is sitting on a horizontal frictionless surface Air resistance is negligible and the collision is elastic During the collision which of the following are conserved

(1) horizontal component of total momentum of ballblock system (2) Total KE of ballblock system(3) Both

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Problem 65 ndash Cutnell and JohnsonA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(a) What is the velocity of the second block after the bullet imbeds itself(b) Find the ratio of the total kinetic energy after the collision to that before the

collision

0513ms

KEAfter KEBefore = 149e-3

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Problem 65 ndash Cutnell and Johnson - extendedA 400-g bullet is moving horizontally with a velocity of +355 ms where the +

sign indicates that it is moving to the right The mass of the first block is 1150 g and its velocity is +0550 ms after the bullet passes through it The mass of the second block is 1530 g

(c) What is the speed of the bullet after the collision with Block 1 and before the collision with Block 2

(d) What is the average force of the bullet on the block if it takes 0400ms to go through block 1

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)

9 if stationary

Initial momentum of system up and to the right

Final momentum same ndash up and to the right

pxi = +(2kg)(3ms) + (1kg)(0ms) ndash (1kg)(3ms) = + 6 kgmiddotms - 3 kgmiddotms = + 3 kgmiddotmspyi = (2kg)(0ms) + (1kg)(3ms) + (1kg)(0ms) = + 3 kgmiddotms

Clicker

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23

ExampleFind the center of mass of the objects shown

1 kg 2 kg1 m

4 kg05 m

• Momentum is a vector Suppose the mass of a block is 2kg If the x-component of the momentum of a block is +4 kgmiddotms and the y-component of the momentum of the block is -3 kgmiddotms what is the speed of the block
• If m=2 kg px = +4 kgms py = -3 kgms What is the magnitude of the momentum of the block
• F versus t graph
• Two balls of equal mass are dropped on the table from the same height Ball A bounces back up to roughly the same height from which it was dropped Ball B does not bounce back up at all Which ball receives the greater impulse from the table
• A 2kg puck is traveling along at 3ms An impulse of 10Ns is exerted on the puck at an angle perpendicular to its motion Which path best describes the motion of the puck after the impulse
• Collisions
• Two small railroad cars are traveling at each other with the masses and speeds shown below If you take the two cars as the system what is the initial total momentum of the system
• After the two cars collide they stick together Which direction will they be traveling (How fast will they be traveling)
• Two cars collide and stick together How fast will they be traveling after the collision
• PowerPoint Presentation
• Slide 13
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignoring friction when they have all linked up as one what is their speed
• Three railroad cars of equal mass are on a track The one on the left is approaching at 6ms Ignore friction At the end the two left cars are linked and traveling at 1ms but the rightmost car didnrsquot connect properly and is free Was is the speed of the separate unlinked car
• Slide 16
• Elastic Collisions
• Example
• Clicker
• Problem 65 ndash Cutnell and Johnson
• Problem 65 ndash Cutnell and Johnson - extended
• Three pucks collide and stick together Initial speeds and masses are given What is the direction of the 3 pucks after the collision (choose an axis only if exactly on that axis)
• Slide 23