Chapter 9. Momentum. Topics: Sample question: Impulse. Momentum. The impulse-momentum theorem Conservation of momentum Inelastic collisions

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1 Chapter 9 Momentum Topics: Impulse Momentum The impulse-momentum theorem Conservation of momentum Inelastic collisions Sample question: Male rams butt heads at high speeds in a ritual to assert their dominance. How can the force of this collision be minimized so as to avoid damage to their brains? Slide 9-1

2 Reading Quiz 1. Impulse is A. a force that is applied at a random time. B. a force that is applied very suddenly. C. the area under the force curve in a force-versus-time graph. D. the interval of time that a force lasts. Answer: C Slide 9-2

3 Reading Quiz 2. The total momentum of a system is conserved A. always. B. if no external forces act on the system. C. if no internal forces act on the system. D. never; momentum is only approximately conserved. Answer: B Slide 9-3

4 Reading Quiz 3. In an inelastic collision, A. impulse is conserved. B. momentum is conserved. C. force is conserved. D. energy is conserved. E. elasticity is conserved. Answer: B Slide 9-4

5 Impulse The force of the foot on the ball is an impulsive force. Slide 9-5

6 Graphical Interpretation of Impulse J = Impulse = area under the force curve Slide 9-6

7 Momentum Momentum is the product of an object s mass and its velocity: p = mv Momentum is a vector Slide 9-7

8 The Impulse-Momentum Theorem Impulse causes a change in momentum: J =p f - p i = p Slide 9-8

9 Example A 0.5 kg hockey puck slides to the right at 10 m/s. It is hit with a hockey stick that exerts the force shown. What is its approximate final speed? Slide 9-9

10 This is a one-dimensional problem... v i = 10 m/s m = 0.5 kg J 1 2 (17 ms 50 N) 425 N ms = kg m/s p i = mv i p i =0.5 kg 10 m/s =5kgm/s p f = p i + p = p i + J p f =5kgm/s kg m/s =5.425 kg m/s v f = p f m kg m/s = 0.5 kg = m/s

11 Checking Understanding Two 1-kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed? A. Ball 1 B. Ball 2 C. Both balls have the same final speed Slide 9-10 Answer: C. Both balls receive the same impulse and have the same mass, so they will have the same final speed.

12 Slide 9-11

13 Example A car traveling at 20 m/s crashes into a bridge abutment. Estimate the force on the driver if the driver is stopped by A. a 20-m-long row of water-filled barrels B. the crumple zone of her car (~1 m). Assume a constant acceleration. Slide 9-12

14 Example A 500 kg rocket sled is coasting at 20 m/s. It then turns on its rocket engines for 5.0 s, with a thrust of 1000 N. What is its final speed? Slide 9-13

15 The Law of Conservation of Momentum In terms of the initial and final total momenta: In terms of components: P f = P i Slide 9-14

16 Slide 9-15

17 Example A curling stone, with a mass of 20.0 kg, slides across the ice at 1.50 m/s. It collides head on with a stationary kg hockey puck. After the collision, the puck s speed is 2.50 m/s. What is the stone s final velocity? Slide 9-16

18 Inelastic Collisions For now, we ll consider perfectly inelastic collisions: A perfectly elastic collision results whenever the two objects move off at a common final velocity. Slide 9-17

19 Example Jack stands at rest on a skateboard. The mass of Jack and the skateboard together is 75 kg. Ryan throws a 3.0 kg ball horizontally to the right at 4.0 m/s to Jack, who catches it. What is the final speed of Jack and the skateboard? Slide 9-18

20 Example A 10 g bullet is fired into a 1.0 kg wood block, where it lodges. Subsequently, the block slides 4.0 m across a floor (µ k = 0.20 for wood on wood). What was the bullet s speed? Slide 9-19

A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. Which fragment has the greater speed?

A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. Which fragment has the greater speed? 1 2 PHYS 1021: Chap. 9, Pg 2 Page 1 1 A uranium nucleus