Chapter 7

Linear Momentum

Objectives: Students will be able to:

• Explain that a conserved quantity is a quantity that remains numerically constant.

• Define and identify situations involving elastic collisions.

• State the law of conservation of momentum and use it to solve one-dimensional collision problems using the appropriate equation.

Exploration Activity

• Collision PHET Lab• Only complete page 1 and part of page 2.

Do not go to inelastic collisions yet.• http://phet.colorado.edu/sims/collision-lab/

collision-lab_en.html

7-4 Conservation of Energy and Momentum in Collisions

Momentum is conserved in all collisions.

Collisions in which kinetic energy is conserved as well are called elastic collisions, and those in which it is not are called inelastic.

Start here

Conservation of Momentum

• When two objects collide, the momentum before the collision must be equal to the momentum after the collision.

• The total momentum of any group of objects remains the same unless outside forces act on the objects.

Conservation of Momentum—Elastic Collisions

After the collision the total momentum of the two vehicles is the same as the car’s before the collision.

Conservation of Momentum—Elastic Collisions

Conservation of Momentum—Elastic Collisions

7-5 Elastic Collisions in One DimensionHere we have two objects colliding elastically. We know the masses and the initial speeds.

Since both momentum and kinetic energy are conserved, we can write two equations. This allows us to solve for the two unknown final speeds.

May 3, 2023

More About Elastic Collisions

• Both momentum and kinetic energy are conserved

• Typically have two unknowns• Momentum is a vector quantity

– Direction is important– Be sure to have the correct signs

• Solve the equations simultaneously

222

211

222

211

22112211

21

21

21

21

ffii

ffii

vmvmvmvm

vmvmvmvm

May 3, 2023

Elastic Collisions• A simpler equation can be used in place of the

KE equation

iffi vvvv 2211

)vv(vv f2f1i2i1

222

211

222

211 2

121

21

21

ffii vmvmvmvm

))(())(( 2222211111 ififfifi vvvvmvvvvm

)()( 222111 iffi vvmvvm

)()( 22

222

21

211 iffi vvmvvm

ffii vmvmvmvm 22112211

ffii vmvmvmvm 22112211

May 3, 2023

Summary of Types of Collisions• In an elastic collision, both momentum and kinetic

energy are conserved

• We will get to inelastic collisions in the next section.• In an inelastic collision, momentum is conserved but

kinetic energy is not

• In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same

iffi vvvv 2211 ffii vmvmvmvm 22112211

ffii vmvmvmvm 22112211

fii vmmvmvm )( 212211

7-5 Elastic Collisions in One Dimension: Example 7-7: Equal masses.

Billiard ball A of mass m moving with speed vA collides head-on with ball B of equal mass at rest (vB = 0). What are the speeds of the two balls after the collision, assuming it is elastic?

(solve together)

7-5 Elastic Collisions in One Dimension

Example 7-8: A nuclear collision. (Try this one.)

A proton (p) of mass 1.01 u (unified atomic mass units) traveling with a speed of 3.60 x 104 m/s has an elastic head-on collision with a helium (He) nucleus (mHe = 4.00 u) initially at rest. What are the velocities of the proton and helium nucleus after the collision? Assume the collision takes place in nearly empty space.

Homework

• Chapter 7 Problems• 22, 23, 25, 27

Closure

• Describe the relationship between kinetic energy and elastic collisions.

• Kahoot