Transcript Physics 102 Introduction to Physics

Chapter 6
Momentum
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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)
Momentum = mass x velocity
(momentum is in the same direction as the velocity)
Momentum is a
vector!!
Momentum = mv
Or
Momentum = mass x speed
(if you don’t care about the direction)
A 20 kg object moving at 10 m/s has a momentum of 200
kg  m
s
Something massive moving fast carries a lot of momentum
Something REALLY massive moving not so fast carries a lot of momentum.
Something with little mass doesn’t carry much momentum unless it goes fast.
Video: Definition of Momentum
Impulse
Given 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 time
Or
Impulse = F x t
A force applied over time will change the momentum of an object:
Impulse examples
Follow through increases the
time of collision and the
impulse
small
large
I
Question 1
Question 1 Answer
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 Momentum
Examples:
Hitting a golf ball:
Baseball and bat:
Apply the greatest force
possible for the longest time
possible.
Accelerates the ball from 0
to high speed in a very short
time.
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 Momentum
It 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
Think about a bouncing ball:
Before it hits the ground: At the moment it hits
Speed = v
the ground:
Momentum = mv
Speed = 0
Momentum = 0
Impulse needed to stop
the ball = mv
After it leaves the ground:
Speed = v
Momentum = mv
Impulse needed to
accelerate the ball
upwoard = mv
Total Impulse = 2mv
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)
Video: Definition of Momentum
Other Bouncing Examples
From book:
Pendulum and block
Pelton Wheel
Also:
Pool Ball off a cushion
(linked to applet)
(Ignore the rotational motion for now)
Flower Pot on Head
Question 1
Question 1 Answer
Conservation of Momentum
If 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
Cannon’s
momentum
Shell’s
momentum
(equal and
opposite)
And after the shot
Cart and bricks applet
After the bricks fall on the cart,
the momentum of the cart-brick
system will still be the same.
Collisions
Net momentum before collision = net momentum after collision
Elastic collisions
- No kinetic energy
lost to heat, etc
2 billiard balls collide head on
momentum is zero before and after
1 billiard balls collide with a stationary one
momentum is the same before and after
2 billiard balls moving in the same direction collide
momentum is the same before and after
Inelastic collisions
- Some kinetic energy
lost to heat, etc
Upon collision, the cars stick together
The 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 Collisions
Colliding at an angle:
Momentum of
car A
The momentum vectors of car A and B add
together to give the resultant momentum of the
system.
The ”exploding object”:
Resultant
Momentum
Momentum of
car A
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.