Chapter 5:Momentum and Its Conservation

California Standards

2d. Students know how to calculate momentum as the product mv.

2. The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:

2f. Students know an unbalanced force on an object produces a change in its momentum.

2e. Students know momentum is a separately conserved quantity different from energy.

2g. Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy.

5.1 Impulse and Momentum

5.1 Objectives

Compare - a system before and after an event in momentum problems.

Define - the momentum of an object.

Recognize - that impulse equals the change in momentum of an object.

Determine and Define - the impulse given to an object.

Concept Development Map

Momentum

Latin momentum =movement, motion, to move

Quantity of Motion

The length of time (power) required to bring the object to rest.

DefinitionsApplications

Linear Momentum

Angular Momentum

Law of Conservation of Momentum

Impulse - Momentum Theorem

What is it?

Motion energy.

Examples

The Normans have momentum.The style is gaining momentum.

Bill Nye the Science Guy(0:00 to 6:20)

Concept Development Map

Impulse

Latin impulsus = in+beatto beat, to strike.to impel, to drive

To act suddenly. Like Nerve impulses

Motion produced by a sudden or momentary force.

DefinitionsApplications

Baseball Bat ball

Tennis Racket and ball

Golf Club and Ball

Boxer’s Punch

What is it?

The product of the average net force exerted on an objectand the time interval over which the force acts.

Examples

Impulse engines.

An impulsive person.

Nerve impulses.

Force versus Impulse

€

F = ma = mΔv

Δt

Starting with Newton’s Second Law:

Multiplying both sides by by t:

€

FΔt = mΔvImpulse = ΔMomentum

F

t

Properties of Impulse

Properties of Momentum

Karate Demo

Defining Impulse and Momentum

€

F =dp

dt

€

Fdt = dp

€

I = F∫ dt = dp∫€

I = FΔt = Δp

€

F =Δp

Δt

€

F =Δmv

Δt

Ouch!!

Ouch!!

Impulse-Momentum Theorem

Expanding the right side:

So, the impulse is equal to the change in momentum:

€

FΔt = mΔv = p2 − p1

€

FΔt = mΔv = mv2 −mv1 = p2 − p1

€

where p = mv = momentum

This is the impulse-momentum theorem.

Join the Chain…

In tennis, the hand exerts a long impulse on the racket, leading to racket momentum.

The racket moves on to create a short impulse on the tennis ball, leading to ball momentum.

The ball moves to the other side of the court where another hand exerts a long impulse on another racket. Then the whole thing starts all over…

Group Discussions…

Break up into table pairs for discussion. Think of, write down, and discuss of as many sports or games that use impulse and momentum as you can. See if you can come up with more than the other groups.

Describe the chain of impulse and momentum that occurs during the sport or game. What provides the impulse? How does the momentum change directions or stop? What design changes might increase the impulse?

Practice Problems

Tiger Woods hits a golf ball (0.046-kg) with a force of 16,000 N for 2x10-4 seconds. At what velocity will the ball leave the club head?€

FΔt = mΔv = mv2 −mv1

Tiger Woods wants to increase the velocity without swinging harder. What can he do to increase the velocity without swinging harder?

Angular Momentum

Replacing with the angular velocity:

Easier to solve for velocity separately, then substitute.€

FΔt = mΔv = mv2 −mv1 = m ac2r2 −m ac1r1

€

where ac =v 2

rleads to v = acr

5.2 The Conservation of

Momentum

Chapter 5.2 Objectives

Recognize - the conditions under which the momentum of a system is conserved.

Relate - Newton’s third law of motion to conservation of momentum in collisions and explosions.

Solve - conservation of momentum problems in two dimensions by using vector analysis.

Apply - conservation of momentum to explain the propulsion of rockets.

Bill Nye the Science Guy(6:20 to 12:05)

Conservation of Momentum

€

mA1vA1 + mB1vB1 = mA 2vA 2 + mBvB 2

In two object collisions, momentum is conserved:

€

pA1 + pB1 = pA 2 + pB 2

€

Beforemomentum = Aftermomentum

Air Track Collisions

Conservation of Momentum

Systems

Closed system - A collection of objects that does not gain or lose mass. >>>>> No in/out; no gain/loss

System - A defined collection of objects.

Open system - A collection of objects that does gain or lose mass. >>>>>> In/out; gain/loss

System Forces

Internal Forces - those forces inside a closed system.

Isolated System - no external forces on a closed system.

External Forces - those forces outside a closed system.

Bill Nye the Science Guy(12:05 to END)