Chapter 6: Chapter 6: Momentum and Collisions!Momentum and Collisions!

The Solar SystemThe Solar System(not to scale!)(not to scale!)

A Question for you to ponder…

Why do the Sun and all of the planets (except Venus) rotate In the same direction?

The Answer lies in the Formation of The Answer lies in the Formation of the Solar Systemthe Solar System

4 billion miles away…do you see 4 billion miles away…do you see what I see?what I see?

That’s us

So What?So What?

What does this have to do with Chapter 6?What does this have to do with Chapter 6?

Planet formation is directly tied to the law of Planet formation is directly tied to the law of conservation of momentum!conservation of momentum!

Yay for more laws Yay for more laws

Linear MomentumLinear Momentum

Momentum describes how the motions of Momentum describes how the motions of objects are changedobjects are changedNewton’s Laws explain Newton’s Laws explain whywhy

The Linear Momentum equationThe Linear Momentum equationp=mvp=mvMomentum = mass x velocityMomentum = mass x velocity

MOMENTUM IS A VECTOR!!MOMENTUM IS A VECTOR!!

Sample ProblemSample Problem

A 3000kg elephant is chasing a 1 kg A 3000kg elephant is chasing a 1 kg squirrel across the road at a velocity of 5 squirrel across the road at a velocity of 5 m/s to the west. What is the momentum of m/s to the west. What is the momentum of the elephant? If the squirrel is running at 7 the elephant? If the squirrel is running at 7 m/s west what is its momentum?m/s west what is its momentum?

Solve the ProblemSolve the Problem

Momentum of the elephantMomentum of the elephantp = mv = (3000 kg)(5m/s)= 15000 kgm/s Westp = mv = (3000 kg)(5m/s)= 15000 kgm/s West

Momentum of the squirrelMomentum of the squirrelp=mv= (1kg)(7m/s)= 7 kgm/s Westp=mv= (1kg)(7m/s)= 7 kgm/s West

Change in MomentumChange in Momentum

A change in momentum takes force and A change in momentum takes force and timetime It takes a lot of force to stop an object that has It takes a lot of force to stop an object that has

a lot of momentuma lot of momentum

Impulse Momentum TheoremImpulse Momentum Theorem

A net external force, A net external force, FF, applied to an , applied to an object for a time interval, object for a time interval, ΔΔt, will cause a t, will cause a change in the object’s momentum equal to change in the object’s momentum equal to the product of the Force and the time the product of the Force and the time interval.interval.

In other words…In other words…

if mvmvptF Impulse

What does that mean?What does that mean?

A small force acting for a long time can A small force acting for a long time can produce the same change in momentum produce the same change in momentum as a large force acting for a short time.as a large force acting for a short time.

In sports like baseball, this is why follow In sports like baseball, this is why follow through is important. The longer the bat is through is important. The longer the bat is in contact with the ball, the greater the in contact with the ball, the greater the change in momentum will be.change in momentum will be.

Sample Problem p. 211 #3Sample Problem p. 211 #3

A 0.40 kg soccer ball approaches a player A 0.40 kg soccer ball approaches a player horizontally with a velocity of 18 m/s north. horizontally with a velocity of 18 m/s north. The player strikes the ball and causes it to The player strikes the ball and causes it to move in the opposite direction with a move in the opposite direction with a velocity of 22 m/s. What impulse was velocity of 22 m/s. What impulse was delivered to the ball by the player?delivered to the ball by the player?

What do we know?What do we know?

M = 0.40 kgM = 0.40 kgVi= +18 m/sVi= +18 m/sVf= -22 m/sVf= -22 m/sWhat does impulse mean?What does impulse mean?

Impulse is equal to FImpulse is equal to FΔΔtt Impulse is also equal to the object’s change in Impulse is also equal to the object’s change in

momentummomentum

Solve the problemSolve the problem

South s

kgm 16or 16

)1822(40.0

s

kgms

m

s

mkgvvmp if

Stopping DistanceStopping Distance

The stopping distance is the distance it The stopping distance is the distance it requires an object to come to restrequires an object to come to rest

The greater the momentum, the more The greater the momentum, the more distance it takes to stopdistance it takes to stop

Sample Problem p.213 #2Sample Problem p.213 #2

A 2500 kg car traveling to the north is A 2500 kg car traveling to the north is slowed down uniformly from an initial slowed down uniformly from an initial velocity of 20.0 m/s by a 6250 N braking velocity of 20.0 m/s by a 6250 N braking force acting opposite the car’s motion. Use force acting opposite the car’s motion. Use the impulse momentum theorem to answer the impulse momentum theorem to answer the following questions:the following questions:

A. What is the car’s velocity after 2.50 s?A. What is the car’s velocity after 2.50 s?B. How far does the car move during 2.50 s?B. How far does the car move during 2.50 s?C. How long does it take the car to come to a C. How long does it take the car to come to a

complete stop.complete stop.

Answer part a.Answer part a.

m= 2500 kgm= 2500 kgVi= 20 m/s NorthVi= 20 m/s NorthF= -6250 NF= -6250 N t= 2.50 st= 2.50 sVf= ?Vf= ?

Why is F negative? Why is F negative?

Because it is acting Because it is acting opposite the car’s opposite the car’s motion!motion!

Use the impulse-momentum Use the impulse-momentum theorem!!theorem!!

North 75.13202500

)50.2)(6250(

s

msv

m

tFV if

tFvvmp if

Solve Part BSolve Part B

How far does the car How far does the car move in 2.5 s?move in 2.5 s?

Which kinematic Which kinematic equation should we equation should we use?use?

N 2.42)5.2)(2075.13(2

1

2

1mstVVx if

tvvx fi 2

1

Solve Part cSolve Part c

How long does it take for the car to come to a How long does it take for the car to come to a complete stop?complete stop?

Use impulse momentum theorem!Use impulse momentum theorem!

s 86250

)20)(2500(0

Nsm

kg

F

mvmv

F

pt if

Summary of 6.1Summary of 6.1

Momentum is a vector quantity that is equal to Momentum is a vector quantity that is equal to the product of an object’s mass and its velocity the product of an object’s mass and its velocity (p=mv)(p=mv)

Impulse = FImpulse = FΔΔt= t= ΔΔpp

A small force applied over a long period of time A small force applied over a long period of time produces the same change in momentum as a produces the same change in momentum as a large force applied over a short period of timelarge force applied over a short period of time

Section 6.2: Conservation of Section 6.2: Conservation of MomentumMomentum

Remember...we talked Remember...we talked about the formation of about the formation of the solar system and the solar system and conservation of conservation of momentum.momentum.

Let’s Talk about the MoonLet’s Talk about the Moon

We are the only inner planet with a We are the only inner planet with a large moon…why?large moon…why?

Our moon didn’t form with us in the nebulaOur moon didn’t form with us in the nebula

We acquired it later through We acquired it later through a collisiona collision with another planetoidwith another planetoid

http://vimeo.com/2015273

The Moon is trying to leave usThe Moon is trying to leave us

Every year, the moon moves about 4 cm away Every year, the moon moves about 4 cm away from the Earth and thus it’s velocity increasesfrom the Earth and thus it’s velocity increases

Conservation of Momentum says that velocity Conservation of Momentum says that velocity has to come from somewhere. So…the moon has to come from somewhere. So…the moon steals it from ussteals it from us

So every year, our rotation slows down… adding So every year, our rotation slows down… adding about 0.0002 seconds to our day.about 0.0002 seconds to our day.

Momentum is ConservedMomentum is Conserved

The Law of Conservation of Momentum The Law of Conservation of Momentum says:says:The total momentum of all objects interacting The total momentum of all objects interacting

with one another remains constant regardless with one another remains constant regardless of the nature of the forces between the of the nature of the forces between the objects.objects.

In mathematical formIn mathematical form

Be very careful with your signs when using Be very careful with your signs when using this equation!!this equation!!

ffii vmvmvmvm ,22,11,22,11

CollisionsCollisions

There are many different ways to describe There are many different ways to describe collisions between objectscollisions between objects In any collision, the total amount of In any collision, the total amount of

momentum is conserved but generally the momentum is conserved but generally the total kinetic energy is not conservedtotal kinetic energy is not conserved

Perfectly Inelastic CollisionsPerfectly Inelastic Collisions

When two objects collide and move together as one When two objects collide and move together as one mass, the collision is perfectly inelasticmass, the collision is perfectly inelastic

Since the two objects stick together and move as Since the two objects stick together and move as one, they have the same final velocity.one, they have the same final velocity.

Kinetic Energy IS NOT CONSERVED in Kinetic Energy IS NOT CONSERVED in PERFECTLY INELASTIC COLLISIONSPERFECTLY INELASTIC COLLISIONS

fii vmmvmvm )( 21,22,11

An 85.0 kg fisherman jumps from a dock An 85.0 kg fisherman jumps from a dock into a 135 kg rowboat at rest on the west into a 135 kg rowboat at rest on the west side of the dock. If the velocity of the side of the dock. If the velocity of the fisherman is 4.30 m/s to the west as he fisherman is 4.30 m/s to the west as he leaves the dock, what is the final velocity leaves the dock, what is the final velocity of the fisherman and the boat?of the fisherman and the boat?

Sample Problem p. 219 #2Sample Problem p. 219 #2

What do we knowWhat do we know

MM11= 85 kg = 85 kg

MM22= 135 kg= 135 kg

VV2,i2,i=0=0

VV1,i1,i= -4.30 m/s= -4.30 m/s

What type of collision is this?What type of collision is this?PERFECTLY INELASTIC because they stick PERFECTLY INELASTIC because they stick

together and move as one masstogether and move as one mass

fii vmmvmvm )( 21,22,11 Rearrange the equation and solve for Rearrange the equation and solve for

VfVf

Vf= 1.66 m/s WestVf= 1.66 m/s West

66.1)85135(

0)3.4)(85(

21

,22,11

sm

kg

mm

vmvmv iif

What is the change in Kinetic What is the change in Kinetic Energy for this problem?Energy for this problem?

Initial Kinetic Energy of the boat= 0 JInitial Kinetic Energy of the boat= 0 J

Initial Kinetic Energy of the fishermanInitial Kinetic Energy of the fisherman KE= 0.5mv^2= 0.5(85kg)(4.3m/s)^2=785.3 JKE= 0.5mv^2= 0.5(85kg)(4.3m/s)^2=785.3 J

Total Initial KE= 0+ 785.3 J= 785.3 JTotal Initial KE= 0+ 785.3 J= 785.3 J

Final KE= 0.5(85+135)(-1.66)^2=303.1 JFinal KE= 0.5(85+135)(-1.66)^2=303.1 J

ΔΔKE=KEKE=KEff – Ke – Keii = 482.2 J = 482.2 J

Elastic CollisionsElastic Collisions

In an elastic collision, two objects collide In an elastic collision, two objects collide and return to their original shapes with no and return to their original shapes with no change in total energy.change in total energy.After the collision, the two objects move After the collision, the two objects move

separately.separately.Momentum is conservedMomentum is conservedKinetic Energy is ConservedKinetic Energy is Conserved

Sample Problem p.229 #2Sample Problem p.229 #2

A 16.0 kg canoe moving to the left at 12 A 16.0 kg canoe moving to the left at 12 m/s makes an elastic head-on collision m/s makes an elastic head-on collision with a 4.0 kg raft moving to the right at 6.0 with a 4.0 kg raft moving to the right at 6.0 m/s. After the collision, the raft moves to m/s. After the collision, the raft moves to the left at 22.7 m/s. Disregard any effects the left at 22.7 m/s. Disregard any effects of the water.of the water.a. Find the velocity of the canoe after the a. Find the velocity of the canoe after the

collision.collision.

What do we know?What do we know?

VV1,i1,i= -12 m/s= -12 m/s

VV2,i2,i = 6 m/s = 6 m/s

VV1,f1,f = ? = ?

V V 2,f2,f = -22.7 m/s = -22.7 m/s

MM11= 16 kg= 16 kg

MM22= 4 kg= 4 kg

Conservation of Momentum says…Conservation of Momentum says…

This is an elastic collision, so we should This is an elastic collision, so we should use the following equation:use the following equation:

ffii vmvmvmvm ,22,11,22,11

Rearrange and solveRearrange and solve

We need to solve for VWe need to solve for V1,f1,f

so we should rearrange so we should rearrange the conservation of the conservation of momentum equationmomentum equation

So The final velocity of the So The final velocity of the canoe is 4.8 m/s Left.canoe is 4.8 m/s Left.

s

m

kgsm

kgsm

kgsm

kgv f 8.4

16

)7.22)(4()6)(4()12)(16(

,1

ffii v

m

vmvmvm,1

1

,22,22,11

Impulse In CollisionsImpulse In Collisions

Think about Newton’s 3rd Law: Every action force has an equal and opposite reaction force

Since Impulse = FΔt then in a collision between objects, the impulse imparted to each mass is the same!!!!

Comparison of CollisionsComparison of CollisionsPerfectly Inelastic Collisions

Inelastic

Collisions

Elastic CollisionsElastic Collisions

Objects stick together and move as one mass after the collision

Momentum is conserved

Kinetic Energy is not conserved because it is converted to other types of energy

Objects are deformed and move separately after the collision

Momentum is conserved

KE is not conserved

Objects return to their original shapes and move separately after the collision

Momentum is conserved

Kinetic Energy is conserved

Summary of Section 6.2 and 6.3Summary of Section 6.2 and 6.3

In all interactions between isolated In all interactions between isolated objects, momentum is conservedobjects, momentum is conserved

Few collisions are elastic or perfectly Few collisions are elastic or perfectly inelasticinelastic

Impulse imparted is the same for all Impulse imparted is the same for all objects in a collisionobjects in a collision