Chapter 8 Momentum

1. Chapter 8 Momentum Conceptual Physics Chapter 8

2. What is Momentum? As you cross the street you notice a large dump truck racing towards you. What is it about the truck that makes it threatening to you? Conceptual Physics Chapter 8

3. Linear Momentum • We can think of momentum as “inertia in motion”. • Momentum is dependant on both mass and velocity. momentum = mass x velocity p = m·v Conceptual Physics Chapter 8

4. Linear Momentum • Momentum is a vector quantity – the direction of the momentum vector will always be the same as the direction of the velocity vector. • Momentum is measured in • Although a stationary object has the same inertia it has when it is moving, it has no momentum when it is stationary. Conceptual Physics Chapter 8

5. Changes in Momentum • Previously we learned that a net force causes a change in velocity. • When the velocity changes, momentum will change. Δp = m·Δv Conceptual Physics Chapter 8

6. Momentum and Newton’s Second Law Newton’s second law tells us By definition, a = m FNET Δv This is called the impulse-momentum relationship. a = Δt Conceptual Physics Chapter 8

7. Impulse-Momentum The left side of the equation, FNETΔt, is called impulse. Impulses cause a change in momentum. Impulse is a vector quantity and is measured in N·s. FNETΔt = mΔv Conceptual Physics Chapter 8

8. Average Force FNETΔt = mΔv Conceptual Physics Chapter 8

9. Increasing Momentum • Momentum can be increased by applying a large force for a long time. • This concept has important applications in athletics. FNET Δt = m Δv Conceptual Physics Chapter 8

10. Decreasing Momentum • The momentum of an object will be decreased when the object is brought to rest. This can be accomplished in one of two ways: A large force may act for a short period of time … or the force can be reduced if the time interval is increased. Either way, the impulse is the same! FNET FNET Δt = = m Δv FNET Δt Δt Conceptual Physics Chapter 8

11. Decreasing Momentum In which case will he experience the larger impulse? In which case does the floor exert a larger force on the man? Regardless of whether the man lands with his knees locked straight or with his knees bent, his final velocity will be zero. In which case will his change in momentum be larger? Conceptual Physics Chapter 8

12. Bouncing • An object experiences a larger change in momentum when bouncing occurs. • The momentum of an object is partially reduced as its velocity is first decreased to zero… …and the momentum is changed even further as the object is forced back in the opposite direction. Conceptual Physics Chapter 8

13. Bouncing A 1000-kg car skids into a concrete wall with a speed of 15 m/s. If the car recoils from the wall at 10 m/s, what is its change in momentum? Δp = m·Δv = 1000 kg (-10 m/s – 15 m/s) = 1000 kg (-25 m/s) = -25000 kg·m/s Conceptual Physics Chapter 8

14. Conservation of Momentum In the absence of an external force, the momentum of a system remains unchanged. Conceptual Physics Chapter 8

15. Conservation of Momentum A bullet is fired from a gun. Which experiences a greater change in momentum, the bullet or the gun? Which is greater, the impulse delivered to the bullet by the gun or the impulse delivered to the gun by the bullet? Which is greater, the force of the gun acting on the bullet or the force of the bullet acting on the gun? Which experiences the greater change in velocity, the bullet or the gun? Which is greater, the time during which the gun exerts a force on the bullet or the time during which the bullet exerts a force on the gun? Conceptual Physics Chapter 8

16. Conservation of Momentum A 1500-kg train car moving at 24 m/s to the right collides with and sticks to an identical train car which is initially stationary. What is the final velocity of each of the two cars? pinitial = pfinal 1500 kg(24 m/s) + 1500 kg(0 m/s)= 1500 kg·v’carA + 1500 kg·v’carB pcarA + pcarB = p’carA + p’carB 1500 kg(24 m/s) + 1500 kg(0 m/s)= (1500 kg + 1500 kg)v’ mcarA vcarA + mcarB vcarB = mcarA v’carA + mcarB v’carB 36000 kg·m/s + 0= (3000 kg)v’ v’= 12 m/s Conceptual Physics Chapter 8

17. Conservation of Momentum Ball A has a mass of 0.5 kg and moves to the right at 2 m/s. Ball B has a mass of 0.7 kg and moves to the left at 2.5 m/s. After the collision, ball B moves to the right at 0.2 m/s. Find the velocity of ball A. pinitial = pfinal mA vA + mB vB = mA v’A + mB v’B 0.5 kg(2 m/s) + 0.7 kg(-2.5 m/s)= 0.5 kg·v’BallA + 0.7 kg(0.2 m/s) 1.0 kg·m/s – 1.75 kg·m/s= 0.5 kg·v’BallA + 0.14 kg·m/s -0.89 kg·m/s= 0.5 kg·v’BallA v’= -1.78 m/s Conceptual Physics Chapter 8

18. Collisions • Momentum is conserved in all collisions (as long as there is no external force acting on the system). • If kinetic energy is also conserved, the collision is said to be elastic. • When kinetic energy of one or both of the bodies is transformed to some other type of energy, the collision is inelastic. Conceptual Physics Chapter 8

19. Elastic Collisions • In an elastic collision there will be no sound, no heat and no deformation of the bodies – kinetic energy is fully conserved. • Perfectly elastic collisions do not occur in the macroscopic world. • The collision of two pool balls is nearly elastic. Conceptual Physics Chapter 8

20. Inelastic Collisions • In an inelastic collision, kinetic energy will be transformed into other types of energy – most commonly heat. • Generally, there will be some sound generated, work done on one or both of the bodies, and occasionally light may be produced. • Most importantly, the colliding bodies stick together and will have a common velocity after the collision. Conceptual Physics Chapter 8

21. Collisions • Most collisions in nature are neither perfectly elastic nor perfectly inelastic – the colliding bodies neither stick together nor do they retain all of their kinetic energy. We call these collisions partially elastic collisions. Conceptual Physics Chapter 8

22. Two-Dimensional Collisions • Momentum is conserved even when interacting objects don’t move along the same straight line. • The momentum of the wreck is equal to the vector sum of the momenta of car A and car B before the collision. Conceptual Physics Chapter 8

23. Two-Dimensional Collisions • When the firecracker bursts, the vector sum of the momenta of its fragments add up to the firecracker’s momentum just before bursting. Conceptual Physics Chapter 8

24. Two-Dimensional Collisions Conceptual Physics Chapter 8

25. Two-Dimensional Collisions Conceptual Physics Chapter 8