impulse momentum the impulse-momentum theorem conservation of momentum inelastic collisions

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

• Impulse

• Momentum

• The impulse-momentum theorem

• Conservation of momentum

• Inelastic collisions

Chapter 9Momentum

Topics:

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


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.

Slide 9-2


1. Impulse is

C. the area under the force curve in a force-versus-time graph.

Slide 9-3

Answer


Impulse

The force of the foot on the ball is an impulsive force.

Slide 9-8


Graphical Interpretation of Impulse

J = Impulse = area under the force curve

=FavgΔt

Slide 9-9


Momentum

Momentum is the product of an object’s mass and its velocity:

Slide 9-10

p = mv


The Impulse-Momentum Theorem

Impulse causes a change in momentum:

Slide 9-11

J =pf - pi = ∆p


Starting and Stopping

A car with a mass of 1 metric ton (1 metric ton = 1000 kg) speeds up to highway speed from rest on a strait section of Central Blvd. A little while later, the car comes to a stop as it approaches a red light.

Left Side - Determine the net impulse and average net force on the car as it goes from rest to highway speed.

Right Side - Determine the net impulse and average net force on the car as it goes from highway speed to a complete stop.

Slide 9-12


Impulses in car crashes

1. Consider a car going at highway speeds colliding in a front-end collision with a brick wall. Rank the impulses needed to bring the passenger in the front seat to a stop if they are stopped separately by:

•Their seatbelt•The dashboard •An airbag

A. Dashboard = Seatbelt = AirbagB. Dashboard > Seatbelt > AirbagC. Airbag > Seatbelt > DashboardD. Dashboard > Airbag > SeatbeltE. Seatbelt > Dashboard > Airbag

Slide 9-12


Impulses in car crashes

2. Consider a car going at highway speeds colliding in a front-end collision with a brick wall. Rank the force being applied for each case. (You will need to think about Delta t. Hint: the longer the distance travelled while the force is being applied, the longer Delta t.)

Slide 9-12


Shut the Door

Imagine that you are sitting on your bed in your dorm room, and suddenly you hear the voice of your ex coming down the hall. You really want to avoid any contact (you broke things off a week ago), and so you want to shut the door. But you don't have time to get up and shut it and act like it wasn't on purpose. You need something fast. Sitting beside you, you happen to have a superball (super bouncy rubber ball) and a ball of clay that you fidget with when you're studying on your bed. What do you do? (Hint: Draw the momentum vectors before and after.)

• Throw the superball• Throw the clay ball• Throw either ball, it doesn’t matter• Not enough information to tell

Explain your answer and show why you chose one and not the other.

Slide 9-12


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 9-12


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 9-13

A. Ball 1B. Ball 2C. Both balls have the same final speed


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 9-14

C. Both balls have the same final speed

Answer


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 9-16


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 9-17


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.

Slide 9-4


2. The total momentum of a system is conserved

B. if no external forces act on the system.

Slide 9-5

Answer


Reading Quiz

3. In an inelastic collision, we make use of the fact that

A. impulse is conserved.

B. momentum is conserved.

C. force is conserved.

D. energy is conserved.

E. elasticity is conserved.

Slide 9-6


3. In an inelastic collision, we make use of the fact that

B. momentum is conserved.

Slide 9-7

Answer


In terms of the initial and final total momenta:

The Law of Conservation of Momentum

In terms of components:

Slide 9-18

Pf = Pi


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 9-20


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 9-21


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 9-22


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 9-23

impulse momentum the impulse-momentum theorem conservation of momentum inelastic collisions

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