Collisions

A B

Conservation of Momentum

A B

During a collision, if the net external force on the system is zero, then the momentum of the system is constant. The momentum of each object in the system will change due to internal forces, but the total momentum of the system remains constant.

Example

A B

mB=1.0 kg and mA=0.5 kg. Initially, cart B is at rest and cart A moves with an x-velocity of 0.25 m/s. After the collision, cart A moves in the -x direction with a speed of 0.04 m/s. What is the velocity of cart B after the collision?

Types of collisions

elastic collision -- kinetic energy is conserved

inelastic collision -- kinetic energy is not conserved

Note: “sticky” collisions are always inelastic. They are called completely inelastic collision.

Sticky Collision

A B

mB=1.0 kg and mA=0.5 kg. Initially, cart B is at rest and cart A moves with an x-velocity of 0.25 m/s. After the collision, the carts stick together. What is their final velocity?

Sticky Collision--Loss of energy

A B

For the previous question, how much kinetic energy is lost due to the collision?

Example

A 250-lb linebacker running with a speed of 0.8 m/s tackles a 200-lb quarterback who is initially at rest. After the collision, they have the same velocity. What is their velocity?

Footall collisions

Impulse

Impulse is defined as

If an object comes to a stop in a short time interval, then the force on the object is LARGE.

If an object comes to a stop in a long time interval, then the force on the object is small.

Longer time interval, smaller force

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Shorter time interval, larger force

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Air bags

smart car crash test

Volvo crash test

Poll

Two carts on a track collide and stick together. Which quantities are conserved during the collision?

1. momentum

2. kinetic energy

3. both momentum and kinetic energy

4. neither momentum nor kinetic energy

Poll

A 300-lb lineman who is running full speed collides with and tackles a 200-lb quarterback who is initially at rest. The magnitude of the change in momentum of the quarterback is

1. less than the magnitude of the change in momentum of the lineman

2. greater than the magnitude of the change in momentum of the lineman

3. equal to the magnitude of the change in momentum of the lineman

Poll

A 300-lb lineman who is running full speed collides with and tackles a 200-lb quarterback who is initially at rest. The magnitude of the change in velocity of the quarterback is

1. less than the magnitude of the change in velocity of the lineman

2. greater than the magnitude of the change in velocity of the lineman

3. equal to the magnitude of the change in velocity of the lineman

Poll

In one case, a superball is thrown at a wall with an initial speed v in the +x direction and rebounds backward with a speed v in the -x direction. In a second case, a piece of clay of the same mass is thrown at the wall and sticks to the wall. On which object is the change in momentum the greatest?

1. superball

2. clay

3. neither, because the impulse on each object is the same

Poll

A rifle lying on the ground at rest discharges and shoots a bullet. The rifle’s mass is of course greater than the bullet’s mass. Which object will have a greater magnitude final momentum?

1. rifle

2. bullet

3. neither, they will have the same momentum

Poll

A rifle lying on the ground at rest discharges and shoots a bullet. The rifle’s mass is of course greater than the bullet’s mass. Which object will have a greater magnitude final velocity?

1. rifle

2. bullet

3. neither, they will have the same momentum

In a crash test, identical vehicles carry identical test dummy “drivers.” Both vehicles are going at 20 m/s (over 40 mi/hr) when they crash head-on into a brick wall and are brought to a stop. Dummy 1’s vehicle has no safety devices. Dummy 2’s vehicle has an air bag that inflates on impact. If we compare the total impulses exerted on the two drivers as each is brought to a stop, the impulse on dummy 2 is ________________ the impulse on dummy 1.A. greater than

B. equal to

C. less than

In a crash test, identical vehicles carry identical test dummy “drivers.” Both vehicles are going at 20 m/s (over 40 mi/hr) when they crash head-on into a brick wall and are brought to a stop. Dummy 1’s vehicle has no safety devices. Dummy 2’s vehicle has an air bag that inflates on impact. If F is the average force exerted on a dummy during its collision, and t is the time interval for which it is exerted, then________________.

A. F is greater on dummy 1 but t is the same for 1 and 2

B. F is greater on dummy 1 but t is greater for dummy 2

C. F is the same on both but t is greater for dummy 2

D. F and t are both greater for dummy 1