Momentum

1. Momentum • Momentum is a vector quantity that can be thought of as inertia in motion. • Depends on two factors, velocity and mass. • Calculated as p = m V where p is momentum, m is mass, and V is velocity. • Calculate the momentum of a 90 kg man running at 3 m/s.

2. Momentum • Calculate the mass of a truck with a momentum of 120,000 kg m/s and a velocity of 58 m/s. • A 8500 kg truck moving at what velocity will have the same momentum as a 3000 kg car moving at 50 m/s. • Which has greater momentum, a 9,000 kg truck at rest or a 7 kg dog moving at 5 m/s?

3. Impulse • An impulse is a force applied for a specific amount of time. • Impulse is calculated as force multiplied by time, or F t. • Units on impulse are the kg m/s2 x s or kg m/s. • What are the units on momentum? • They have the same units. Impulse causes momentum.

4. Impulse • When we apply a force, such as a baseball bat, to a ball, we are giving it an impulse. • What happens to the momentum of the ball? • This leads to the impulse-momentum theorem which states that Ft = mV. • If a 200 N force is applied to a 0.15 kg ball for 0.3 seconds, what will the velocity be? • A 90 N force is applied to a 30 kg grocery cart for 4 seconds. Calculate the speed of the cart.

5. Impulse and momentum • Calculate the momentum of a 1 kg ball moving at 20 m/s to the left. • It hits the wall a bounces to the right at 20 m/s. What is the momentum of the ball now? • What was the change in momentum? • A 0.3 kg ball moving at 40 m/s is caught by a catcher exerting a force of 60 N. How long does it take to stop the ball?

6. Give one, get one • You are going to seek out other students to get additional examples of impulse and momentum • Write this question on your sheet. “Describe a real world case of how impulse creates a change in momentum.” • Find 9 other students to add a different idea to your sheet as you add to theirs. • Describe two of these examples in detail in a paragraph.

7. Practice • Calculate the momentum of a 600 kg motorcycle moving at 40 m/s. • Calculate the force the engine exerted if it takes 3 seconds to achieve this speed. • Calculate the force exerted by friction if the bike coasts to a stop in 24 seconds. • A 0.15 kg ball moving at 35 m/s to the left hits a wall and bounces back to the right at 20 m/s. Assuming the ball is in contact with the wall for 0.15 seconds, calculate the force the wall exerts.

8. Effect of time on impulse • How do we increase the momentum of an object if we can only apply a certain amount of force? • This is called time of contact. • If we increase the time of contact, what happens to the impulse? The momentum? • Why do coaches insist on “follow through”?

9. Effect of time on impulse • Suppose your car brakes fail while driving. You must stop the car because the bridge is out ahead. On the left side is a large tree. On the right is a large group of bushes. Which way do you turn and why? • When jumping from a stage to the floor below, we bend our knees on landing. Why? • How do air bags help us survive collisions? • Why do we bend our knees when we jump up straight in the air?

10. Collisions • Momentum is conserved in a collision if no other forces act on the colliding bodies. • This is virtually impossible in the real world. • When objects collide, sound is produced, heat is generated, the objects bend, or sparks fly. All of these use energy. • In physics, we ignore these other forces. • There are two types of collisions, elastic and inelastic. They are solved in very different ways.

11. Collisions • Elastic collisions are those where the objects collide and bounce off each other with NO LOSS of energy. • Inelastic collisions are those where the colliding objects stick together with NO LOSS of energy. Neither occurs in nature. • Real world collisions are said to be partially inelastic.

12. Elastic collisions • Let’s look at three cases: a moving object strikes a stationary object, a moving object strikes a moving object coming at it, and a moving object strikes a slower object moving in the same direction.

13. Inelastic collisions • In an inelastic collision, we combine the momentums and the masses to solve the problem. • We will again look at three cases: a moving object strikes a stationary object, a moving object strikes a moving object coming at it, and a moving object strikes a slower object moving in the same direction.

14. LHP • What is an elastic collision? • Show the step by step solution of the elastic collision where two balls of 20 kg and 30 kg that are heading toward each other at speeds of 5 m/s and 8 m/s respectively.

15. Practice • A car with a mass of 3000 kg and a velocity of 50 m/sec strikes a truck with a mass of 7000 kg moving in the same direction at 35 m/sec. Calculate the velocity of the car and truck assuming 1). A completely elastic collision and 2). A completely inelastic collision

16. Practice • A car with a mass of 3000 kg and a velocity of 50 m/sec strikes a truck with a mass of 7000 kg moving in the opposite direction at 35 m/sec. Calculate the velocity of the car and truck assuming 1). A completely elastic collision, and 2). A completely inelastic collision.

17. Practice • In an elastic collision, ball number one is rolling at 25 m/s and strikes ball two rolling at 10 m/s in the opposite direction. What is the speed of ball one and two after the collision? The mass of ball one is 20 kg and ball two is 10 kg.

18. Practice • In an elastic collision, ball number one (with a mass of 40 kg) is rolling at 120 m/s catches up and strikes ball two (with a mass of 10 kg) rolling at 15 m/s in the same direction. What are the speeds of ball one and two after the collision?

19. Practice • If two objects with masses of 20 kg and 30 kg roll toward each other at 15 m/s each and become involved in a completely inelastic collision, what is the velocity of the resulting pair?

20. LHP • How does an elastic collision differ from an inelastic collision? • Show the step by step solution of the inelastic collision where two balls of 20 kg and 30 kg that are heading toward each other at speeds of 5 m/s and 8 m/s respectively.