MomentumMomentum

Chapter 8Chapter 8

ObjectivesObjectives Define momentum.Define momentum. Define impulse and describe how it affects Define impulse and describe how it affects

changes in momentum.changes in momentum. Explain why an impulse is greater when an Explain why an impulse is greater when an

object bounces than when the same object object bounces than when the same object comes to a sudden stop.comes to a sudden stop.

State the law of conservation of momentum.State the law of conservation of momentum. Describe how conservation of momentum Describe how conservation of momentum

applies to collisions.applies to collisions. Describe how the vector nature of Describe how the vector nature of

momentum affects the law of conservation momentum affects the law of conservation of momentum.of momentum.

8.1 Momentum8.1 Momentum Momentum is a Momentum is a

commonly used term commonly used term in sports.in sports. A team that has “the A team that has “the

momentum" or has “a momentum" or has “a lot of momentum” is on lot of momentum” is on the move and is going the move and is going to take some effort to to take some effort to stop. stop.

In Physics, momentum In Physics, momentum means “inertia in means “inertia in motion” or “mass in motion” or “mass in motion”.motion”.

Momentum Momentum (p)(p) = =

mass mass (m)(m) x velocity x velocity (v)(v)

p =p = mvmv Momentum is a vector quantity Momentum is a vector quantity

with it’s direction matching that with it’s direction matching that of the velocity.of the velocity.

When direction is not important:When direction is not important: Momentum = mass x speedMomentum = mass x speed

The The units for momentumunits for momentum would would be mass units times velocity be mass units times velocity units. units. The standard metric unit of The standard metric unit of

momentum is the kg*m/s.momentum is the kg*m/s.

p = mvp = mv The equation illustrates that momentum The equation illustrates that momentum

is is directly proportionaldirectly proportional to an object's to an object's mass and mass and directly proportionaldirectly proportional to the to the object's velocity.object's velocity.

A moving object can have a large A moving object can have a large momentum if momentum if it has a large mass.it has a large mass. it has a high speed.it has a high speed. it has a large mass and a high speed.it has a large mass and a high speed.

PracticePractice What is the momentum of a 1500 kg What is the momentum of a 1500 kg

car traveling at 20 m/s?car traveling at 20 m/s? What is the momentum of the car if What is the momentum of the car if

the speed is reduced by ½?the speed is reduced by ½? What is the momentum of a 3000 kg What is the momentum of a 3000 kg

truck traveling at 20 m/s?truck traveling at 20 m/s? What is the truck’s momentum if its What is the truck’s momentum if its

speed doubles?speed doubles? Can the car ever have the same or Can the car ever have the same or

more momentum than the truck? more momentum than the truck? Explain.Explain.

8.2 Impulse Changes 8.2 Impulse Changes MomentumMomentum

If the momentum of an object changes, If the momentum of an object changes, either the either the massmass or the or the velocityvelocity, or , or bothboth, , has to change.has to change.

The mass usually does not change; The mass usually does not change; therefore, the therefore, the velocity must changevelocity must change..

What do we call a change in velocity?What do we call a change in velocity? An acceleration is a change in velocityAn acceleration is a change in velocity..

What produces an acceleration?What produces an acceleration? A FORCE produces acceleration!A FORCE produces acceleration!

8.2 Impulse Changes 8.2 Impulse Changes MomentumMomentum

Since a = F/m, the greater the force, the Since a = F/m, the greater the force, the greater the acceleration.greater the acceleration.

But recall that a = But recall that a = ΔΔv/t ; so, a greater v/t ; so, a greater acceleration means a greater change in acceleration means a greater change in velocity.velocity.

If p = mv, a greater change in velocity If p = mv, a greater change in velocity will mean a greater change in will mean a greater change in momentum!momentum!

The greater the force, the greater the The greater the force, the greater the change in momentum.change in momentum.

8.2 Impulse Changes 8.2 Impulse Changes MomentumMomentum

A change in momentum A change in momentum depends on a force that depends on a force that acts and acts and alsoalso the length the length of time that it acts!of time that it acts!

A brief contact by a A brief contact by a defensive football defensive football player will change the player will change the momentum of the momentum of the offensive player.offensive player.

However, if the same However, if the same force is applied over a force is applied over a longer time period, a longer time period, a greater change in greater change in momentum will occur.momentum will occur.

8.2 Impulse Changes 8.2 Impulse Changes MomentumMomentum

The quantity of “force x time interval” is called The quantity of “force x time interval” is called impulse.impulse.

The greater the impulse exerted on something, The greater the impulse exerted on something, the greater will be the change in momentum.the greater will be the change in momentum.

Impulse = change in momentum.Impulse = change in momentum.

Increasing MomentumIncreasing Momentum In order to increase the In order to increase the

momentum of the ball, the momentum of the ball, the player needs to apply the player needs to apply the greatest force possible for greatest force possible for as long as possible – it is as long as possible – it is necessary to swing hard necessary to swing hard and follow through.and follow through.

Since the force applied Since the force applied here (and in situations like here (and in situations like this) changes throughout this) changes throughout the swing, we really mean the swing, we really mean the the average force.average force.

In each situation above, the truck experiences a change In each situation above, the truck experiences a change in momentum to 0. The impulse for each is the same.in momentum to 0. The impulse for each is the same.

In situation 1, by traveling through the haystack, the In situation 1, by traveling through the haystack, the truck truck increases the timeincreases the time interval for the change. The interval for the change. The force the truck experiences, therefore, is relatively small.force the truck experiences, therefore, is relatively small.

On the other hand, in situation 2, the time interval is On the other hand, in situation 2, the time interval is very short, so the force the truck experiences is very very short, so the force the truck experiences is very large.large.

DecreasingMomentum

More ExamplesMore Examples

If a boxer moves away If a boxer moves away from a punch, the from a punch, the contact time of the contact time of the punch is increased and punch is increased and the force is decreased. the force is decreased. If he moves towards If he moves towards the punch, the time of the punch, the time of contact is reduced and contact is reduced and force is increased.force is increased.

Crumple zones are sections Crumple zones are sections in cars which are designed in cars which are designed to crumple up when the car to crumple up when the car encounters a collision. encounters a collision. Crumpling of the car Crumpling of the car lengthens the time over lengthens the time over which the car's momentum which the car's momentum is changed; by increasing is changed; by increasing the time of the collision, the the time of the collision, the force of the collision is force of the collision is greatly reduced. greatly reduced.

PracticePractice When a dish falls, will the impulse be less When a dish falls, will the impulse be less

if it lands on a carpet than if it lands on a if it lands on a carpet than if it lands on a hard floor?hard floor?

Explain why Explain why a padded dashboard is safer than a rigid one.a padded dashboard is safer than a rigid one. airbags save lives.airbags save lives. you should bend your knees when jumping you should bend your knees when jumping

from a height.from a height. bungee cords must be elastic.bungee cords must be elastic.

If a bungee cord increases contact time by If a bungee cord increases contact time by 10 times over a non elastic cord, how 10 times over a non elastic cord, how much is the force that acts on the jumper much is the force that acts on the jumper reduced? reduced?

8.3 Bouncing8.3 Bouncing

Bouncing is also known as rebounding.Bouncing is also known as rebounding. What affect does bouncing or rebounding What affect does bouncing or rebounding

have on a change in momentum?have on a change in momentum?

8.3 Bouncing8.3 Bouncing Impulses (or changes in momentum) are Impulses (or changes in momentum) are

greater when an object bounces.greater when an object bounces. An impulse is needed to bring a moving object to a An impulse is needed to bring a moving object to a

stop.stop. Another impulse is needed to then “throw” the Another impulse is needed to then “throw” the

object back into motion.object back into motion. For example, your head could provide an For example, your head could provide an

impulse to a falling object, reducing its impulse to a falling object, reducing its momentum to 0. To then throw the object momentum to 0. To then throw the object back up into the air, your head would need to back up into the air, your head would need to provide another impulse. It takes a greater provide another impulse. It takes a greater impulse to catch and throw back an object impulse to catch and throw back an object than to just catch it.than to just catch it.

8.3 Bouncing8.3 Bouncing An object that An object that

bounces can yield as bounces can yield as much as 2x the much as 2x the impulse to the object impulse to the object it bounces off.it bounces off.

Karate experts strike Karate experts strike bricks, for example, bricks, for example, in such a way that in such a way that their hand bounces their hand bounces back. The impulse to back. The impulse to the bricks can be up the bricks can be up to 2x as much.to 2x as much.

See Figures 8.8 & 8.9 See Figures 8.8 & 8.9 in your text, p. 130.in your text, p. 130.

8.4 Conservation of Momentum8.4 Conservation of Momentum

According to Newton’s 2According to Newton’s 2ndnd Law, you accelerate an Law, you accelerate an object by applying a net force to it.object by applying a net force to it.

In momentum, to change the momentum of an In momentum, to change the momentum of an object, you exert an impulse on it.object, you exert an impulse on it.

In either case, internal forces won’t work.In either case, internal forces won’t work. If you sit in a car and push on the dashboard, the car If you sit in a car and push on the dashboard, the car

will not move. The momentum of the car does not will not move. The momentum of the car does not change.change.

Pushing on the outside of the car, though, may cause Pushing on the outside of the car, though, may cause the car to move. An external force does change the car to move. An external force does change momentum.momentum.

8.4 Conservation of Momentum8.4 Conservation of Momentum The momentum before The momentum before

firing is 0.firing is 0. After firing, the force on the After firing, the force on the

cannonball is equal and cannonball is equal and opposite to the force on the opposite to the force on the cannon, so the momentum cannon, so the momentum of the cannon-cannonball of the cannon-cannonball system does not change. system does not change. The net momentum is still The net momentum is still 0.0.

Net momentum is neither Net momentum is neither gained nor lost.gained nor lost.

8.4 Conservation of Momentum8.4 Conservation of Momentum In every case, momentum of a system does not In every case, momentum of a system does not

change unless the system is acted on by an outside change unless the system is acted on by an outside force.force.

Momentum, therefore, is Momentum, therefore, is conservedconserved.. The The law of conservation of momentumlaw of conservation of momentum states that, in states that, in

the absence of an external force, the momentum of a the absence of an external force, the momentum of a system remains unchanged.system remains unchanged. If a system undergoes an internal change, the net If a system undergoes an internal change, the net

momentum of the system before and after the event is the momentum of the system before and after the event is the same.same.

In a collision, for example, the net momentum of the In a collision, for example, the net momentum of the cars before the collision must equal their net cars before the collision must equal their net momentum after the collisionmomentum after the collision..

8.5 Collisions8.5 Collisions A collision is A collision is elasticelastic when objects collide when objects collide

without being permanently deformed and without being permanently deformed and without generating heat.without generating heat. Some heat is generated in most collisions. For our Some heat is generated in most collisions. For our

purposes, we will consider it negligible.purposes, we will consider it negligible. At the atomic level, collisions are generally At the atomic level, collisions are generally

perfectly elastic.perfectly elastic. Colliding objects Colliding objects bouncebounce perfectly in elastic perfectly in elastic

collisions.collisions. The sum of the momentum of the objects that The sum of the momentum of the objects that

collide is the same before and after the collide is the same before and after the collision.collision.

net momentumnet momentumbefore collsionbefore collsion = net momentum = net momentumafter collisionafter collision

A l000 kg car traveling 20 m/s strikes a 3000 kg truck at A l000 kg car traveling 20 m/s strikes a 3000 kg truck at rest. What is the velocity of the car after the collision if rest. What is the velocity of the car after the collision if the velocity of the truck is 10 m/s?the velocity of the truck is 10 m/s?

First, determine the momentum before the collision.First, determine the momentum before the collision.

net momentumnet momentumbefore collsionbefore collsion = car mom. = car mom.beforebefore + truck mom. + truck mom.beforebefore = = m mcar beforecar beforevvcar beforecar before + m + mtruck beforetruck beforevvtruck beforetruck before

SET UP A MOMENTUM TABLE.SET UP A MOMENTUM TABLE.

Elastic Collisions: Sample ProblemElastic Collisions: Sample Problem

Elastic Collisions: Sample ProblemElastic Collisions: Sample Problem A l000 kg car traveling 20 m/s strikes a 3000 kg A l000 kg car traveling 20 m/s strikes a 3000 kg

truck at rest. What is the velocity of the car after truck at rest. What is the velocity of the car after the collision if the velocity of the truck is 10 m/s?the collision if the velocity of the truck is 10 m/s?

Momentum BEFORE

MomentumAFTER

(1000)(20) = 20000 kg-m/s

(3000)(0) =0 kg-m/s

20000 kg-m/s

CAR

TRUCK

TOTAL

Problem ContinuedProblem Continued

Next, determine the momentum after the collision.Next, determine the momentum after the collision.

momentum before = momentum after = 20000 kg m/smomentum before = momentum after = 20000 kg m/s

FILL IN THE TOTAL IN THE AFTER COLUMNFILL IN THE TOTAL IN THE AFTER COLUMN Then, fill in the information you have about “after”. Then, fill in the information you have about “after”.

Use a variable to represent what you don’t know.Use a variable to represent what you don’t know.

momentummomentumafter collisionafter collision = car mom. = car mom.afterafter + truck mom. + truck mom.afterafter

= m= mcar aftercar aftervvcar aftercar after + m + mtruck aftertruck aftervvtruck aftertruck after

A l000 kg car traveling 20 m/s strikes a 3000 kg A l000 kg car traveling 20 m/s strikes a 3000 kg truck at rest. What is the velocity of the car truck at rest. What is the velocity of the car after the collision if the velocity of the truck is after the collision if the velocity of the truck is 10 m/s?10 m/s?

Momentum BEFORE

MomentumAFTER

(1000)(20) = 20000 kg-m/s

(1000)v

(3000)(0) =0 kg-m/s

(3000)(10) =30,000 kg-m/s

20000 kg-m/s 20000 kg-m/s

CAR

TRUCK

TOTAL

A l000 kg car traveling 20 m/s strikes a 3000 kg A l000 kg car traveling 20 m/s strikes a 3000 kg truck at rest. What is the velocity of the car truck at rest. What is the velocity of the car

after the collision if the velocity of the truck is after the collision if the velocity of the truck is 10 m/s?10 m/s?

Finally, solve the algebraic expression that was Finally, solve the algebraic expression that was created in the after column.created in the after column.

1000v + 30000 = 200001000v + 30000 = 20000

v = -10 m/sv = -10 m/s

The car bounced back off the truck in the opposite The car bounced back off the truck in the opposite direction!!direction!!

PracticePractice

A 3000 kg truck traveling at 20 m/s collides A 3000 kg truck traveling at 20 m/s collides with a 1000 kg car at rest.? If the velocity of with a 1000 kg car at rest.? If the velocity of the truck after the collision is 10 m/s, what is the truck after the collision is 10 m/s, what is the velocity of the car?the velocity of the car?

A 1000 kg car collides head on with a 3000 kg A 1000 kg car collides head on with a 3000 kg truck. Both vehicles are traveling at 20 m/s. If truck. Both vehicles are traveling at 20 m/s. If the truck stops completely upon collision, what the truck stops completely upon collision, what is the resulting velocity of the car?is the resulting velocity of the car?

PracticePractice

Inelastic CollisionsInelastic Collisions In an In an inelastic collisioninelastic collision, the colliding , the colliding

objects become distorted and generate heat objects become distorted and generate heat during the collision.during the collision.

A totally inelastic collision occurs when the A totally inelastic collision occurs when the colliding objects become tangled or “stick” colliding objects become tangled or “stick” together.together.

Here, as well, the net momentum before is Here, as well, the net momentum before is equal to the net momentum after the equal to the net momentum after the collision.collision.

net momentumnet momentumbefore collsionbefore collsion = net momentum = net momentumafter collisionafter collision

A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg truck. If they stay coupled, what is the velocity of the car truck. If they stay coupled, what is the velocity of the car and truck after the collision?and truck after the collision?

Use a momentum table (as before). The only difference is Use a momentum table (as before). The only difference is that the velocity of the car AND truck after collision is not that the velocity of the car AND truck after collision is not known. HOWEVER, you do know it is THE SAME!known. HOWEVER, you do know it is THE SAME!

Inelastic Collisions: Sample ProblemInelastic Collisions: Sample Problem

A 1000 kg car traveling 20 m/s strikes a A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg truck. If they stay coupled, stationary 3000 kg truck. If they stay coupled, what is the velocity of the car and truck after what is the velocity of the car and truck after

the collision?the collision?

Momentum BEFORE

MomentumAFTER

(1000)(20) = 20000 kg-m/s

(1000)v

(3000)(0) =0 kg-m/s

(3000)(v)

20000 kg-m/s 20000 kg-m/s

CAR

TRUCK

TOTAL

A 1000 kg car traveling 20 m/s strikes a A 1000 kg car traveling 20 m/s strikes a stationary 3000 kg truck. If they stay coupled, stationary 3000 kg truck. If they stay coupled, what is the velocity of the car and truck after what is the velocity of the car and truck after

the collision?the collision?

As before, use the table to set up an As before, use the table to set up an algebraic equation. Then solve it!algebraic equation. Then solve it!

1000v + 3000v = 200001000v + 3000v = 20000

4000 v = 200004000 v = 20000

v = 5 m/sv = 5 m/s

A 3000 kg truck traveling at 20 m/s collides with A 3000 kg truck traveling at 20 m/s collides with a 1000 kg car at rest. After collision, the a 1000 kg car at rest. After collision, the vehicles stick and move off together. At what vehicles stick and move off together. At what velocity do the vehicles travel after the velocity do the vehicles travel after the collision?collision?

PracticePractice

A 1000 kg car traveling at 20 m/s collides head A 1000 kg car traveling at 20 m/s collides head on with a 3000 kg truck, traveling at 20 m/s as on with a 3000 kg truck, traveling at 20 m/s as well. The collision is not elastic. What is the well. The collision is not elastic. What is the velocity of the car and truck after collision?velocity of the car and truck after collision?

PracticePractice

8.5 Collisions8.5 Collisions

Most collisions usually do involve Most collisions usually do involve some external force: friction. some external force: friction. Moving objects will encounter friction Moving objects will encounter friction

with a surface and the air.with a surface and the air. Friction provides an impulse to Friction provides an impulse to

decrease the momentum of moving decrease the momentum of moving objects.objects.

External forces, however, are External forces, however, are negligible negligible duringduring a collision. Net a collision. Net momentum, therefore, is unaffected.momentum, therefore, is unaffected.

8.6 Momentum Vectors8.6 Momentum Vectors Momentum is conserved even when Momentum is conserved even when

interacting objects don’t move along the interacting objects don’t move along the same straight line.same straight line.

8.6 Momentum Vectors8.6 Momentum Vectors

The vector sum of the momenta is The vector sum of the momenta is the same before and after a collision.the same before and after a collision. This means we must use vector addition This means we must use vector addition

to determine the sum of the momenta of to determine the sum of the momenta of the 2 cars (previous slide) before they the 2 cars (previous slide) before they collide.collide.

This “net momentum” is the same as This “net momentum” is the same as the net momentum after the collision.the net momentum after the collision.

8.6 Momentum Vectors8.6 Momentum Vectors

Recall that we can use Recall that we can use the Pythagorean the Pythagorean theorem to find the theorem to find the value of the resultant value of the resultant vector.vector.

(20000)(20000)22 + (10000) + (10000)22 = = RR22

R = 22,361 kg m/s R = 22,361 kg m/s

NORTHEASTNORTHEAST

20000 kg m/s EAST

100

00 k

g

m/s

NO

RT

H

RESULTANT

PracticePractice

A 1000 kg car traveling east at 15 A 1000 kg car traveling east at 15 m/s is struck by a 1000 kg car m/s is struck by a 1000 kg car traveling north at 15 m/s. What is traveling north at 15 m/s. What is the net momentum after the the net momentum after the collision? collision?