Chapter 6Momentum

• Impulse

• Impulse Changes Momentum

• Bouncing

• Conservation of Momentum

• Collisions

Momentum Momentum: Inertia in motion - or - mass in motion .

Carries the notion of both mass (inertia) and velocity (motion)

Video: Definition of Momentum

Momentum = mass x velocity(momentum is in the same direction as the velocity)

Momentum = mv

Or

Momentum = mass x speed (if you don’t care about the direction)

Something massive moving fast carries a lot of momentumSomething REALLY massive moving not so fast carries a lot of momentum.

Something with little mass doesn’t carry much momentum unless it goes fast.

Momentum is a vector!!

A 20 kg object moving at 10 m/s has a momentum ofs

mkg 200

ImpulseGiven that … Momentum = mv

If velocity changes, momentum changes, and acceleration (either + or –) occurs

But we know:1. for acceleration to occur, a force has to be applied.

2. If a given force is applied over a longer time, more acceleration occurs.

IMPULSE is a measure of how much force is applied for how much time, and it’s equal to the change in momentum.

Impulse = Force x timeOr

Impulse = F x t

A force applied over time will change the momentum of an object:

Impulse examples

                      I small large

Follow through increases the time of collision and the impulse

Question 1

Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs?1. Impulses.2. Accelerations.3. Momentum changes.4. All of these occur in equal and opposite pairs.5. None of these do.

Question 1 Answer

1. Impulses.2. Accelerations.3. Momentum changes.4. All of these occur in equal and opposite pairs.5. None of these do.

Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs?

Impulse changes Momentum

A greater impulse exerted on an object A greater change in momentum

OR

Impulse = Change in momentum

OR

Impulse = Δ(mv)Greek symbol “Delta”

Means “the change in…”

Impulse can be exerted on an object to either INCREASE or DECREASE its momentum.

Case 1: Increasing MomentumExamples:

Hitting a golf ball:Apply the greatest force possible for the longest time possible.Accelerates the ball from 0 to high speed in a very short time.

Baseball and bat:The impulse of the bat decelerates the ball and accelerates it in the opposite direction very quickly.

Video: Changing Momentum – Follow Through

Case 2: Decreasing MomentumIt takes an impulse to change momentum, and

Remember … Impulse = F x t

If you want to stop something’s motion, you can apply a LOT of force over a short time,

Or, you can apply a little force over a longer time.

Remember, things BREAK if you apply a lot of force to them.

Case 3: Decreasing Momentum over a Short Time

If the boxer moves away from the punch, he extends the time and decreases the force while stopping the punch.

If he moves toward the punch, he decreases the time and increases the force

The airbag extends the time over which the impulse is exerted and decreases the force.

Hitting the bricks with a sharp karate blow very quickly maximizes the force exerted on the bricks and helps to break them.

Bouncing

Video: Definition of Momentum

Important point: It only takes an impulse of mv to stop the ball. It takes twice that much (2mv) to make it bounce)

(Maybe why basketballs don’t bounce so well on gravel)

Think about a bouncing ball:

Before it hits the ground:Speed = v

Momentum = mv

At the moment it hits the ground:Speed = 0

Momentum = 0

After it leaves the ground:Speed = v

Momentum = mv

Impulse needed to stop the ball = mv

Total Impulse = 2mv

Impulse needed to accelerate the ball upwoard = mv

Other Bouncing ExamplesFrom book:

Pendulum and block Pelton Wheel Flower Pot on Head

Also:

Pool Ball off a cushion (linked to applet)

(Ignore the rotational motion for now)

Question 1

An ice sailcraft is stalled on a frozen lake on a windless day. A large fan blows air into the sail. I f the wind produced by the fan strikes and bounces backward from the sail, thesailcraft will move

1. to the left (backward).2. to the right (forward).3. not at all.

Question 1 Answer

1. to the left (backward).2. to the right (forward).3. not at all.

An ice sailcraft is stalled on a frozen lake on a windless day. A large fan blows air into the sail. I f the wind produced by the fan strikes and bounces backward from the sail, thesailcraft will move

Conservation of MomentumIf no net external force (same as saying “no net impulse”) acts on a system, the system’s momentum cannot change.

Momentum = 0 before the shot

And after the shotCannon’s

momentumShell’s

momentum (equal and opposite)

Cart and bricks applet

After the bricks fall on the cart, the momentum of the cart-brick system will still be the same.

CollisionsNet momentum before collision = net momentum after collision

Elastic collisions- No kinetic energy lost to heat, etc

Inelastic collisions- Some kinetic energy lost to heat, etc

2 billiard balls collide head onmomentum is zero before and after

1 billiard balls collide with a stationary onemomentum is the same before and after

2 billiard balls moving in the same direction collide momentum is the same before and after

Upon collision, the cars stick togetherThe total mass moves slower, but the momentum of the 2 cars together is the same as the momentum of the system before the collision.

More Complicated CollisionsColliding at an angle:

The ”exploding object”:

The momentum vectors of car A and B add together to give the resultant momentum of the system.

Momentum of car A

Mo

me

ntu

m o

f ca

r A Resultant

Momentum

The firecracker is initially falling

After the explosion, the momenta of the pieces add.The total momentum of the “system” of pieces is the same as the original momentum of the firecracker.