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Momentum. the quantity of motion. § 8.1–8.2. What’s the point?. Nature keeps careful account of momentum. Think Question. Which process will require more time ?. Pulling as hard as you can to accelerate a little red wagon from rest to a speed of 1 m/s.

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Momentum

Momentum

the quantity of motion

§ 8.1–8.2


What s the point
What’s the point?

  • Nature keeps careful account of momentum.


Think question
Think Question

Which process will require more time?

  • Pulling as hard as you can to accelerate a little red wagon from rest to a speed of 1 m/s.

  • Pulling as hard as you can to accelerate a horse trailer from rest to a speed of 1 m/s.

  • The two take the same amount of time.


Think question1
Think Question

Which process will require more force?

  • Accelerating a little red wagon from rest to a speed of 1m/s in ten seconds

  • Accelerating a horse trailer from rest to a speed of 1m/s in ten seconds.

  • The two take the same force.


Impulse

Impulse = FDt

where

F Is net force

Dt is duration

Impulse

Effect of a force over time

Impulse is a vector.


Think question2
Think Question

Two objects of different masses move at the same velocity. Which one is harder to stop?

The light object.

The massive object.


Think question3
Think Question

Two objects with the same mass move different speeds. Which one is harder to stop?

The fast object.

The slow object.


Momentum1

p = mv

Momentum

Formula

momentum is a vector.


Whiteboard work
Whiteboard Work

Prove that when a net force F is applied to an object of mass m for a time Dt, its change in momentum is

Dp = FDt


Impulse momentum theorem
Impulse–Momentum Theorem

  • Impulse = FDt.

  • FDt

= maDt

= mDv

  • So FDt = D(mv) = change in momentum


Newton s second law

dp

F =

dt

Newton’s second law

As Newton had it:


Poll question
Poll Question

Which changes its momentum the most?

  • A moving object that stops when it hits a barrier.

  • A moving object that bounces back from a barrier.

Hints:

Momentum is a vector.

Which receives the greater impulse?


Rebound and momentum

final p – initial p

final p – initial p

initial p

initial p

Dp

Dp

final p

final p= 0

Rebound and Momentum


Poll question1
Poll Question

Which changes its kinetic energy the most?

  • A moving object that stops when it hits a barrier.

  • A moving object that bounces back from a barrier.

Hints:

Kinetic energy is a scalar.

Which has the greater net work done?


Conservation of momentum

Conservation of Momentum

Here today, somewhere tomorrow

§ 8.2


Poll question2
Poll Question

If a 0.25-g insect collides with a 1250-kg compact car, which experiences the greatest impulse in the collision?

The insect.

The car.

It’s a tie.

Insufficient information to answer.

Hint: Remember Newton’s third law.


Poll question3
Poll Question

If a 0.25-g insect collides with a 1250-kg compact car, which experiences the greatest momentum change in the collision?

The insect.

The car.

It’s a tie.

Insufficient information to answer.

Hint:Remember the impulse-momentum theorem.


Conservation of momentum1
Conservation of Momentum

  • Newton’s first law:

    • no outside force

    • no change in v

    • thus no change in p

  • So an isolated object’s momentum never changes.


Conservation of momentum2

Conservation of Momentum

  • Newton’s third law:

    • interacting objects apply equal and opposite impulses to each other

    • they experience equal and opposite momentum changes

  • So the sum of their momenta remains the same.


Conservation of momentum3
Conservation of Momentum

The total momentum of an isolated system never changes.


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