Chapter 6: Momentum

1. Chapter 6: Momentum 12.1 Momentum 12.2 Force is the Rate of Change of Momentum 12.3 Angular Momentum

2. Chapter 12 Objectives Calculate the linear momentum of a moving object given the mass and velocity. Describe the relationship between linear momentum and force. Solve a one-dimensional elastic collision problem using momentum conservation. Describe the properties of angular momentum in a system—for instance, a bicycle. Calculate the angular momentum of a rotating object with a simple shape.

4. Chapter Vocabulary • angular momentum • collision • law of conservation of • momentum • elastic collision • gyroscope • impulse • inelastic collision • linear momentum • momentum

5. Inv 12.1 Momentum Investigation Key Question: What are some useful properties of momentum?

6. 12.1 Momentum • Momentum is a property of moving matter. • Momentum describes the tendency of objects to keep going • Net forces change momentum.

7. 12.1 Momentum • The momentum depends on mass and velocity. • Ball B has more momentum than ball A.

8. 12.1 Momentum • If both ball A and B were pushed with the same force, what can we determine about their difference?

9. 12.1 Kinetic Energy and Momentum • Kinetic energy and momentum are different, even though both depend on mass and speed. • Kinetic energy is a scalar quantity. • Momentum is a vector, so it always depends on direction.

10. p = m v 12.1 Calculating Momentum Momentum (kg m/sec) Velocity (m/sec) Mass (kg)

11. Comparing momentum Calculate and compare the momentum of the car and motorcycle. • You are asked for momentum. • You are given masses and velocities. • Use: p = m v • Solve for car: p = (1,300 kg) (13.5 m/s) = 17,550 kg m/s • Solve for cycle: p = (350 kg) (30 m/s) = 10,500 kg m/s • The car has more momentum even though it is going much slower.

12. 12.1 Conservation of Momentum • The law of conservation of momentum states that without an outside force, the total momentum of the system is constant. If you throw a rock forward from a skateboard, you will move backward in response.

14. 12.1 Conservation of Momentum

15. 12.1 Collisions in One Dimension • A collisionis when two or more objects hit each other. • During a collision, momentum is transferred • Collisions can be elastic orinelastic.

17. 12.1 Collisions

18. Inelastic collisions What is their combined velocity after the collision? • You are asked for the final velocity. You are given masses, and initial velocity of moving train car. • Diagram the problem, use m1v1 + m2v2 = (m1v1 +m2v2) v3 • Solve for v3= (8,000 kg)(10 m/s) + (2,000 kg)(0 m/s) (8,000 + 2,000 kg) v3= 8 m/s

19. The Archer • An archer at rest on frictionless ice fires a 0.5-kg arrow horizontally at 50.0 m/s. The combined mass of the archer and bow is 60.0 kg. With what velocity does the archer move across the ice after firing the arrow?

20. 12.1 Collisions in 2 and 3 Dimensions • Most real-life collisions do not occur in one dimension. • In order to analyze two-dimensional collisions you need to look at each dimension separately. • Momentum is conserved separatelyin the xand ydirections.

21. 12.1 Collisions in 2 and 3 Dimensions

23. Investigation Key Question: How are force and momentum related? 12.2 Force is the Rate of Change of Momentum

24. 12.2 Force is the Rate of Change of Momentum • Momentum changes when a net force is applied. • The inverse is also true: • If momentum changes, forces are created. • If momentum changes quickly, large forces are involved.

25. F = D p D t 12.2 Force and Momentum Change The relationship between force and motion follows directly from Newton's second law. Force (N) Change in momentum (kg m/sec) Change in time (sec)

26. Calculating force • You are asked for force exerted on rocket. • You are given rate of fuel ejection and speed of rocket • Solve: Δ = (100 kg) (-2,500 m/s) = -250,000 kg m/s • Use F = Δ ÷ΔtSolve: ΔF = (100 kg) (-250,000 kg m/s) ÷(1s)= - 25,000 N • The fuel exerts and equal and opposite force on rocket of +25,000 N. Starting at rest, an 1,800 kg rocket takes off, ejecting 100 kg of fuel over a second at a speed of 2,500 m/sec.Calculate the force on the rocket from the change in momentum of the fuel.

27. 12.2 Impulse • Impulse measures a change in momentum because it is not always possible to calculate force and time individually • Collisions happen so fast!

28. F D t = D p 12.2 Force and Momentum Change To find the impulse, you rearrange the momentum form of the second law. Impulse (N•sec) Change in momentum (kg•m/sec) Impulse can be expressed in kg•m/sec (momentum units) or in N•sec.

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30. 12.2 Impulse • What is the change of momentum between these two balls? • Impulse = change in v * time • aka change in momentum

31. 12.2 Impulse • What is the change of momentum between these two balls? • Rubber ball change in velocity is 4. • Clay one the change is 2. • So the rubber ball had twice as much impulse

32. 12.2 Impulse • So things that bounce have a great impulse, so they feel a greater force!

33. 12.2 Impulse • You are given a choice at a carnival game of what ball to throw at stacked milk jugs. • Sandbag which stops when it hits • A base ball which goes through • And a rubber ball which bounces

34. 12.2 Impulse Which one do you choose? • Sandbag which stops when it hits • A base ball which goes through • And a rubber ball which bounces • Take a vote

35. 12.2 Impulse • You choose the rubber ball because the change in momentum is the most • so the impulse is bigger. • This means the force the ball feels is more. • And with equal and opposite the jugs feel more force too!

36. 12.2 Impulse • But which ball do they let you use in this game?

38. 12.2 Impulse • This is why carnivals are evil