Aim: How can we apply conservation of Aim: How can we apply conservation of momentum to collisions?momentum to collisions?

Identify conservation laws that you know.Identify conservation laws that you know.

Conservation of MomentumConservation of Momentum

In a system, the momentum of the In a system, the momentum of the individual components may change, but individual components may change, but the total momentum of the system remains the total momentum of the system remains constant.constant.

Law of Conservation of Momentum:Law of Conservation of Momentum: ppbeforebefore = p = pafter after (in reference table)(in reference table)How is this useful?How is this useful?

Identifying termsIdentifying terms

afterbefore pp

1 2 1 2

Before Collision After Collision

Car AccidentCar Accident

A 1,000-kg car moving at 5 m/s collides A 1,000-kg car moving at 5 m/s collides into a 1200-kg car at rest. After the into a 1200-kg car at rest. After the collision the 1000 kg car comes to rest.collision the 1000 kg car comes to rest.Calculate the velocity of the 1200kg car after Calculate the velocity of the 1200kg car after

the collision.the collision.Calculate the total momentum before and Calculate the total momentum before and

after the collision.after the collision.

SolutionSolution

momentum before = momentum aftermomentum before = momentum after

ppbeforebefore = p = pafter after

s

mv 17.4'2

)'(1200)0(1000 2vkgs

mkg )0(1200)5(1000

s

mkg

s

mkg

2211 vmvm '' 2211 vmvm

0/5000 skgm )(12000 '2vkg

A 1,000 kg car is moving to the right at 12 A 1,000 kg car is moving to the right at 12 m/s. Another 1500kg car is moving to the m/s. Another 1500kg car is moving to the left. The cars collide and are brought to left. The cars collide and are brought to rest. Determine the initial speed of the rest. Determine the initial speed of the 1500 kg car.1500 kg car.

A 0.005 kg bullet is moving to the right at A 0.005 kg bullet is moving to the right at 200 m/s. The bullet strikes a stationary 200 m/s. The bullet strikes a stationary block of wood on a frictionless, level block of wood on a frictionless, level surface. The mass of the wood block is surface. The mass of the wood block is 7.0 kg. The bullet travels right through 7.0 kg. The bullet travels right through the wood and continues out the other side the wood and continues out the other side with a speed of 150 m/s. with a speed of 150 m/s.

1. Calculate the speed of the block after 1. Calculate the speed of the block after the collision.the collision.

2. What is the direction of the block after 2. What is the direction of the block after the collision?the collision?

A 0.26-kg cue ball moving at 1.2 m/s A 0.26-kg cue ball moving at 1.2 m/s strikes a stationary 0.17-kg 8 ball. After the strikes a stationary 0.17-kg 8 ball. After the collision the cue ball comes to rest.collision the cue ball comes to rest.

A) Calculate the magnitude of the velocity A) Calculate the magnitude of the velocity of the 8 ball after the collision. of the 8 ball after the collision.

B) Determine the total momentum after the B) Determine the total momentum after the collision. collision.

A 1.0-kg ball traveling north at 3.0 m/s A 1.0-kg ball traveling north at 3.0 m/s collides with a 4.0-kg ball at rest. collides with a 4.0-kg ball at rest. Determine the magnitude of the total Determine the magnitude of the total momentum after the collision. momentum after the collision.

SummarySummaryDescribe the conservation of momentum.Describe the conservation of momentum. Identify the formula for conservation of Identify the formula for conservation of

momentum.momentum.A 5-kg bowling ball rolling at 3m/s collides A 5-kg bowling ball rolling at 3m/s collides

into a 6.2-kg ball at rest. After the collision into a 6.2-kg ball at rest. After the collision the 5-kg ball comes to rest.the 5-kg ball comes to rest.A) Calculate the speed of the 6.2-kg ball after A) Calculate the speed of the 6.2-kg ball after

the collision.the collision.B) If the time of impact is .23 seconds, B) If the time of impact is .23 seconds,

determine the force exerted on the 6.2-kg ball.determine the force exerted on the 6.2-kg ball.

Aim: How can we calculate final Aim: How can we calculate final velocity after a collision?velocity after a collision?

A 2-kg object moving at 5 m/s collides with A 2-kg object moving at 5 m/s collides with a 4-kg object at rest. After the collision the a 4-kg object at rest. After the collision the 2-kg object comes to rest.2-kg object comes to rest.A) Calculate the velocity of the 4-kg object A) Calculate the velocity of the 4-kg object

after the collision.after the collision.B) If the time of impact was .01 seconds then B) If the time of impact was .01 seconds then

what is the force exerted on the 4kg object?what is the force exerted on the 4kg object? Is the force exerted on the 2-kg object the Is the force exerted on the 2-kg object the

same? Why?same? Why?

A 5.0-kilogram steel block is at rest. A 1.5-A 5.0-kilogram steel block is at rest. A 1.5-kilogram lump of clay is propelled at kilogram lump of clay is propelled at 5.0m/s at the steel block. After the collision 5.0m/s at the steel block. After the collision the clay sticks to the steel block. Calculate the clay sticks to the steel block. Calculate the speed after the collision. (hint: sketch a the speed after the collision. (hint: sketch a picture)picture)

Bullet and BlockBullet and Block

A 0.1-kilogram bullet is fired horizontally A 0.1-kilogram bullet is fired horizontally with a velocity of 400m/s into a 14.6-kg with a velocity of 400m/s into a 14.6-kg wooden block at rest. The bullet is wooden block at rest. The bullet is imbedded in the wooden block. Determine imbedded in the wooden block. Determine the speed of the block after impact.the speed of the block after impact.

A 2.0-kg object is moving at 3m/s to the A 2.0-kg object is moving at 3m/s to the right and a 4.0-kg object is moving at 8m/s right and a 4.0-kg object is moving at 8m/s to the left on a horizontal frictionless table. to the left on a horizontal frictionless table. If the two objects collide and stick together If the two objects collide and stick together after the collision then what is the after the collision then what is the final final total momentumtotal momentum? ?

Summary:Summary:

1) How can we describe an inelastic 1) How can we describe an inelastic collision?collision?

2) Explain what happens to the masses 2) Explain what happens to the masses after the collision.after the collision.

Aim: How can we apply Aim: How can we apply conservation of momentum to the conservation of momentum to the

recoil/explosion problem?recoil/explosion problem?A 0.1-kilogram bullet is fired horizontally at A 0.1-kilogram bullet is fired horizontally at

350m/s into a 5-kg wooden block at rest. 350m/s into a 5-kg wooden block at rest. The bullet is imbedded in the wooden The bullet is imbedded in the wooden block. Determine the speed of the block block. Determine the speed of the block after impact.after impact.

http://www.youtube.com/watch?v=x71pa_YWgbQ

A hunting rifle fires a bullet of mass A hunting rifle fires a bullet of mass 0.00953 kg with a velocity of 500 m/s to0.00953 kg with a velocity of 500 m/s tothe right. The rifle has a mass of 4 kg.the right. The rifle has a mass of 4 kg.Calculate the recoil speed of the rifle as Calculate the recoil speed of the rifle as the bullet leaves the rifle.the bullet leaves the rifle.

A 62.1-kg male ice skater is facing a 42.8-A 62.1-kg male ice skater is facing a 42.8-kg female ice skater. They are at rest on kg female ice skater. They are at rest on the ice. They push off each other and the ice. They push off each other and move in opposite directions. The female move in opposite directions. The female skater moves backwards with a speed of skater moves backwards with a speed of 3.11 m/s. Determine the speed of the male 3.11 m/s. Determine the speed of the male skater. skater.

A rock is hammered into two pieces. A 0.25-kg A rock is hammered into two pieces. A 0.25-kg piece flies to the left at 5 m/s, while the other 0.5 piece flies to the left at 5 m/s, while the other 0.5 kg piece flies to the right. How fast does the kg piece flies to the right. How fast does the second piece fly?second piece fly?

SummarySummary

Describe the total momentum before the Describe the total momentum before the explosion/recoil.explosion/recoil.

Identify the formula for recoil/explosion Identify the formula for recoil/explosion formula. formula.

Explain conservation of momentum.Explain conservation of momentum.

Aim: How can we apply Aim: How can we apply conservation of momentum to conservation of momentum to

head on collisions?head on collisions?

How can we describe the types of How can we describe the types of head on collisions?head on collisions?

Inelastic Inelastic ElasticElastic

A 900kg car traveling west at 20 m/s A 900kg car traveling west at 20 m/s collides head on with a 1,000kg car collides head on with a 1,000kg car traveling east. Immediately after the traveling east. Immediately after the collisions the cars come to rest.collisions the cars come to rest.Determine the initial speed of the Determine the initial speed of the

1,000kg car.1,000kg car.

A 850kg car traveling north at 15 m/s A 850kg car traveling north at 15 m/s collides with a 2,000kg car traveling south. collides with a 2,000kg car traveling south. After the collision the 850kg car rolls south After the collision the 850kg car rolls south at 4 m/s. The 2,000kg car come to rest.at 4 m/s. The 2,000kg car come to rest.Determine the initial speed of the 2,000kg car. Determine the initial speed of the 2,000kg car.

A 2,000kg truck traveling at 30m/s east A 2,000kg truck traveling at 30m/s east collides with a 10,000kg bus traveling collides with a 10,000kg bus traveling west. The vehicles lock at move together west. The vehicles lock at move together at 7 meters per second west.at 7 meters per second west.Calculate the initial speed of the bus.Calculate the initial speed of the bus.

Summary:Summary:

How do we determine if the collision is How do we determine if the collision is inelastic or elastic?inelastic or elastic?

Describe the total momentum before and Describe the total momentum before and after a collision. after a collision.

Aim: How can we apply conservation of Aim: How can we apply conservation of momentum to applications?momentum to applications?

A 300 kg motorcycle moving at 15m/s east A 300 kg motorcycle moving at 15m/s east collides with a 900 kg car at rest. After the collides with a 900 kg car at rest. After the collision the 900kg car moves at 6m/s east collision the 900kg car moves at 6m/s east and the 300 kg motorcycle rolls west.and the 300 kg motorcycle rolls west.A) Determine the final speed of the A) Determine the final speed of the

motorcycle.motorcycle.B) If the time of impact was 0.85 seconds B) If the time of impact was 0.85 seconds

then calculate the force.then calculate the force.C) Calculate the impulse.C) Calculate the impulse.