MomentumMomentum – Key Ideas– Key Ideas

Review – If a force Fx is applied to abody over a displacement x, theproduct Fx x = (Fcos)x = Work

Review – If a force Fx is applied to abody over a displacement x, theproduct Fx x = (Fcos)x = Work

If the friction force is less than Fx, the work increases the object’s Kinetic Energy

2 2o

1 12 2netW KE m m

NOW ask: What is the effect of applyinga force over a time interval?

Vocabulary: events in which objects apply forces to each other are called

INTERACTIONS

NOW ask: What is the effect of applyinga force over a time interval?

Vocabulary: events in which objects apply forces to each other are called

INTERACTIONS

You predicted the outcomes of someinteractions..

How did you do?

You predicted the outcomes of someinteractions..

How did you do?

A general rule about interaction forces:

A general rule about interaction forces:

Forces come in

12 21F F

A general rule about interaction forces:

Forces come in

12 21F F

This is Newton’s 3rd Law.

The product of mass and velocity

(a quantity) is called

(symbol: )

ve

Definition

t

c or

:

moment p

m

um

p

Newton's second law (one force):

Rearrange:

F ma mt

F t m

Impulse = Change of momentum

Newton's second law (one force):

Rearrange:

F ma mt

F t m

Impulse = Change of momentum

Newton meter (N mUni ) = kg m st:

The impulse is the area under the force vs. time curve. The average force gives the same impulse to the object in the time interval Δt as the real time-varying force.

Conservation of Momentum

The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system remains constant in time.

Specifically, the total momentum before the collision will equal the total momentum after the collision.

Conservation of Momentum

Mathematically: 1 2 2 1 2 2f fm m m m

Momentum is conserved for the system of objects.The system includes all the objects interacting with each other.Assumes only internal forces are acting during the collision.Can be generalized to any number of objects.

Force as a function of time for the two colliding particles.

In all collisions, total momentum is conserved.

We consider two types of collisions in one dimension:

1. Totally elastic

2. Totally inelastic

Perfectly Inelastic Collisions

When two objects stick together after the collision, they have undergone a perfectly inelastic collision.

Conservation of momentum becomes

1 2 22

1 2 1 2

1 2 12

1 2 2 1 2 2

1 2

1

2 1 2 2

2 1 2

Final vel

1 1 1 1

2 2 2 2

2

2

ocities:

f f

f f

f i

f i

m m m m

m m m

m m m m

m m m

m m

m m m m

m m

1 2 2 1 2i i fm m m m

Elastic Collisions

Both momentum and kinetic energy are conserved.

1 2 22

1 2 1 2

1 2 12

1 2 2 1 2 2

1 2

1

2 1 2 2

2 1 2

Final vel

1 1 1 1

2 2 2 2

2

2

ocities:

f f

f f

f i

f i

m m m m

m m m

m m m m

m m m

m m

m m m m

m m