Chien-ch9.PDF Linear Momentum and Collisions

7/28/2019 Chien-ch9.PDF Linear Momentum and Collisions

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AP Review Sheet 1: Chapter 9 Linear Momentum & Collisions

[Background]

This chapter covers the use of Newtons third law in physics, allowing us to consider theramifications of elastic, inelastic, and perfectly inelastic collisions in two dimensions. This

chapter also covers the calculation of the center of mass of non-symmetrical objects.

Key Terms

Linear Momentumdefined as the vector

quantity which describes the amount of inertia

that a particular object has based upon its mass

and velocity.

Corresponding formula: Isolated SystemIn an isolated system,

the total momentum of the system does not

change.

Impulsedefined as the change in momentum

or as the force applied to an object over time.

Corresponding formula: Conservation of MomentumUniversal law

that prohibits the creation of momentum fromnothing.

Non-isolated SystemIn a non-isolated system, a force may add or remove momentum from a

system by applying a force over time.

Elastic CollisionA collision in which kinetic energy is conserved.

Corresponding formulae: #1: ,#2: ,#3:

Inelastic CollisionA collision in which energy is lost, either to heat or sound.Corresponding formula: Perfectly Inelastic CollisionA collision in which objects stick together.

Corresponding formula: Center of MassA point at which a systems mass can be said to be concentrated at.


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[Diagram]

Remember that in elastic collisions as shown above, the angle of deflection between the two

colliding bodies is equal to 90 in two dimensions.

[Review Questions]

1) A 60 kg ice skater jumps from the rink at an angle of 30 above the horizontal, with a speedof 5 m/s. Her partner of mass 70 kg catches her at the top of her arc, moving with an initial

velocity of 6 m/s in the same direction. Assume air friction is negligible. What is their finalvelocity?

2) A cue ball weighing 170g is hit from rest with a cue, and thereafter attains a velocity of 2 m/s.The collision lasts .0015 seconds. What is the force felt by the cue ball? The cue ball nowcollides with another billiard ball of equal mass, which is moving with a velocity of -3 m/s.

The cue ball is deflected from its original path by -15. If the cue ball is moving with a speed

of .5 m/s, what is the final velocity of the billiard ball??

3) A metal ballbearing is shot out of a cannon at 10 m/s. It immediately is caught by apendulum that is .1 m long and has a mass of .5 kg. This pendulum rotates 12 before coming

to a halt. What is the mass of this ballbearing? Suppose its initial velocity was 15 m/s?


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30

Rearrange change of momentum

equation

Plug in and solve

[Solutions and Explanations]1) A 60 kg ice skater jumps from the rink at an angle of 30 above the horizontal, with a

speed of 5 m/s. Her partner of mass 70 kg catches her at the top of her arc, moving withan initial velocity of 6 m/s in the same direction. Assume air friction is negligible. What

is their final velocity?

() ()

2) A cue ball weighing 170g is hit from rest with a cue, and thereafter attains a velocity of 2m/s. The collision lasts .0015 seconds. What is the force felt by the cue ball? The cue ballnow collides with another billiard ball of equal mass, which is moving with a velocity of-3 m/s. The cue ball is deflected from its original path by -15. If the cue ball is moving

with a speed of .5 m/s, what is the final velocity of the billiard ball??

( )

( ) ( )

( )

( ) (()()()())

() ()

We have to solve for her

horizontal velocity alone. Perfectly inelastic collision

formula Plug in, solve for vf

A slightly longer version of the formula for elastic collisions, allowing for calculation in 2-D

Solve for v2f

, keeping in mind that the angle of deflection is 90


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h

LL-h

Exaggerated scale for demonstration12

3) A metal ballbearing is shot out of a cannon at 10 m/s. It immediately is caught by apendulum that is .1 m long and has a mass of .5 kg. This pendulum rotates 12 before comingto a halt. What is the mass of this ballbearing? Suppose its initial velocity was 15 m/s?

() ,

( ) ()

or 10.6 g

( ) ()

or 7.00 g

We must work backwards from the

energy analysis to find the velocityof the catch and ball right after the

perfectly elastic collision.

Cancel ms and solve for v. Howto find h?

Now we go through the processagain, this time with v1i=15 m/s

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Chien-ch9.PDF Linear Momentum and Collisions