# Momentum

Momentum is mass in motion. Anything with mass that is moving has momentum. An impulse causes a change in momentum. The change of momentum produced by an impulse is equal to the impulse in both magnitude and direction. Impulse = average force x change in time. In most problems we assume that a constant force acts for a certain amount of time. The SI units are N*s.

The linear momentum (p) of a body is the product of its mass (m) and velocity (v).

**p = m**

Remember that momentum, as velocity, is a vector. The SI units of momentum are kg*m/s.

The "impulse-momentum theorem" states that impulse equals change in momentum of:

**Ft= umv = mvfinal - mvinitial**

Momentum is always conserved in a collision and kinetic energy is sometimes conserved. If the net external force acting on a system of objects is zero, the vector sum of the moments of the objects will remain constant.

In collisions and explosions, the vector sum of the momenta just before the event equals the vector sum of the momenta just after the event. The vector sum of the momenta of the objects involved does not change during the collision or explosion. Thus, when two bodies of masses (m1 and m2) collide, the total momentum before impact is equal to the total momentum after impact.

### An **elastic **collision (billiard balls) is one where kinetic energy is conserved. The objects do not stick together.

### An inelastic collision is one in which kinetic energy is not conserved. The objects stick together in an inelastic collision.

### What is the velocity of grandma and the boy after the collision?

*v = 4 m/s *

### Which blow is going to do the most damage?

*The large force over a short time. *

### What is the velocity of the train cars after the collision?

*4 m/s. *

### What is the velocity of the truck after the collision?

### *5 m/s *

### Review Questions:

1. DeWayne buys a They Might Be Giants CD at the mall and races home in his car to play it at home. On the way home, he realizes that he left it at the mall and hits his brakes hard for 2.0s. As a result, the average force of 5.0 x 103N is exerted on his car to slow it. What is the momentum?

*1.0 x 10*4 kg*m/s *

2. Dan accelerates a 240.0 kg jet ski, which results in a force being exerted that speeds the jet ski up from 6.00 m/s to 28.0 m/s over a time interval of 60.0s. (a) What is the impulse on the jet ski? (b) What is the magnitude of the average force that is exerted on the jet ski?

a. 5.28 x 10*3 kg*m/s

b. 88.0 N

3. Eric hits a 0.144 kg baseball that is pitched by David at 38 m/s. After it is hit by the bat, it moves at the same speed, but in the opposite direction. (a) What was the change in momentum of the ball? (b) What was the impulse delivered by the bat? (c) If the bat and ball were in contact for 0.80 ms, what was the average force the bat exerted on the ball?

a. 10.9 kg*m/s

b. 10.9 kg*m/s

c. 1.4 x 10*4 N

4. Aklilu weighs 60 kg and drives his car into a concrete wall after his brakes fail. His car is 220 kg and is traveling at 94 km/h before the crash. The car does not rebound from the wall. The velocity of Aklilu equals that of the car both before and after the crash, and the velocity changes in 0.20s. (a) What is the average force exerted on Aklilu? (b) He thinks that he can stop himself from flying forward by putting his hands on the dashboard. What is the mass of an object that would have a weight equal to the force calculated in a. Could he lift such a mass? Is Aklilu strong enough to stop himself with his arms?

a. 8 x 10*3 N

b. F=mg so m = 800 kg which is too heavy to lift. He cannot safely stop himself with his arms.

5. A 0.105 kg hockey puck moving at 24 m/s is caught by William, a 75 kg goalie at rest. With what speed does William slide on the ice?

0.034 m/s

6. A 35.0 g bullet strikes a 5.0 kg stationary wooden block and embeds itself in the block. The block and bullet fly off together at 8.6 m/s. What was the original speed of the bullet?

1.2 x 10*3 m/s

7. A 35.0 g bullet moving at 475 m/s strikes a 2.5 wooden block that is at rest. The bullet passes through the block, leaving at 275 m/s. How fast is the block moving when the bullet leaves?

2.8 m/s

8. Belinda's brother has a mass of 35.6 kg and he has a 1.3 kg skateboard. What is the combined momentum of her brother and his skateboard if they are going 9.50 m/s?

351 kg*m/s

9. Cassie crashes her car through a barrier at 10 m/s and stops in 0.050s. There is a 20 kg child riding on her lap in the car. Assume that the child's velocity is changed by the same amount as the car's in the same period. (a) What is the impulse needed to stop the child? (b) What is the average force on the child? (c) What is the approximate mass of an object whose weight equals the force in b? (d) Could Cassie lift such a weight with her arms? (e) Why is it advisable to use a proper infant restraint rather than hold a child on her lap?

a. 2.0 x 10*2 kg*m/s

b. 4.0 x 10*3 N

c. 4.1 x 10*2 kg

d. No!

e. She could not protect the child on her lap in the event of a collision.

10. Andy is practicing for an upcoming ballet with Nely. He is 60 kg and leaps 0.32 m high. (a) With what momentum does Andy reach the ground? (b) What impulse is needed to stop him? (c) As Andy lands, his knees bend, lengthening the stopping time to 0.050s. What is the average force exerted on his body? (d) Compare the stopping force to his weight.

a. 1.5 x 10*2 kg*m/s down

b. 1.5 x 10*2 N*s up

c. 3 x 10*3 N

d. Weight is 6 x 10*2 N so the stopping force is about five times his weight