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Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
• Impulse
• Momentum
• The impulse-momentum theorem
• Conservation of momentum
• Inelastic collisions
Chapter 9MomentumTopics:
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Reading Quiz
1. Impulse isA. 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.
Slide 9-2Answer: C
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Reading Quiz
2. The total momentum of a system is conservedA. 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.
Slide 9-3Answer: B
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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.
Slide 9-4Answer: B
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Impulse
The force of the foot on the ball is an impulsive force.
Slide 9-5
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Graphical Interpretation of Impulse
J = Impulse = area under the force curve
Slide 9-6
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Momentum
Momentum is the product of an object’s mass and its velocity:
Slide 9-7
p = mv→ →
Momentum is a vector
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
The Impulse-Momentum Theorem
Impulse causes a change in momentum:
Slide 9-8
J =pf - pi = ∆p→ → →→
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
pi = 0.5 kg × 10 m/s = 5 kg m/s
J ≈ 1
2(17 ms× 50 N)
≈ 425 N ms = 0.425 kg m/s
pf = pi +∆p
pi = mvi
pf = 5 kg m/s + 0.425 kg m/s = 5.425 kg m/s
vf =pfm
=5.425 kg m/s
0.5 kg
= pi + J
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
This is a one-dimensional problem...
= 10.85 m/s
vi = 10 m/sm = 0.5 kg
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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?
Slide 9-10
A. Ball 1B. Ball 2C. Both balls have the same final speed
Answer: C. Both balls receive the same impulse and have the same mass, so they will have the same final speed.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-11
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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.
Example
Slide 9-12
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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?
Example
Slide 9-13
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
In terms of the initial and final total momenta:
The Law of Conservation of Momentum
In terms of components:
Slide 9-14
Pf = Pi→→
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 9-15
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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 0.160-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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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 (µk = 0.20 for wood on wood). What was the bullet’s speed?
Slide 9-19