Download Momentum

Momentum
And its
Conservation
Momentum
Momentum is defined as mass times
velocity.
Momentum is represented by the
symbol p, and is a vector quantity.
p = mv
momentum = (mass)( velocity)
the SI units are mass & velocity combined
(kg x m/s)
Bowling ball or basketball?
Picture two lanes at a
bowling alley.
One with a bowling ball
the other with a
basketball going at the
same speed.
Which will exert more
force on the pins?
Why?
More momentum
Momentum
Example
A 2250 kg pickup truck has a velocity of
25 m/s to the east. What is the momentum
of the truck?
p = mv
p = (2250 kg)(25 m/s east)
p = 5.6 x 104 kg x m/s to the east
Momentum
2) A deer with a mass of 146 kg is running
head-on toward you at a speed of 17 m/s.
You are going north find the momentum of
the deer.
p = 2482 kg*m/s south
3) A 21 kg child on a 5.9 kg bike is riding
with a velocity of 4.5 m/s to the
northwest.
a) What is the total momentum of the child
and the bike together?
b) What is the momentum of the child?
c) What is the momentum of the bike?
Conservation of
Momentum
So far we only have considered the
momentum
of only one object at a time.
Now we will look at two or more objects
interacting with each other.
Picture this. . .You are playing pool. You
strike the cue ball it hits the 8 ball. The
8 ball had no momentum before they
collided.
During the collision the cue ball loses
momentum and the 8 ball gains
momentum.
The momentum the cue ball loses is the
same amount that the 8 ball gained.
Conservation of
Momentum
The Law of Conservation of Momentum:
The total momentum of all objects
interacting with one another remains
constant regardless of the nature of the
forces between the objects.
total initial momentum = total final momentum
p1i + p2i = p1f + p2f
m1v1,i + m2v2,i = m1v1,f + m2v2,f
Momentum is Conserved
The total momentum of all objects
interacting with one another remains
constant regardless of the nature of the
forces between the objects.
Go back to the pool table example.
The cue ball and the 8 ball do not have a
constant momentum, but the total
momentum is constant.
Momentum is Conserved
Picture this . . .
Two people on skates
facing one another. They
push away from one
another. Initially, they are
both at rest with a
momentum of 0. When
the push away, they
move in opposite
directions with equal but
opposite momentum, so
that the total momentum
is unchanged and still 0.
Little Problem
A 76 kg boater, initially A 76 kg boater, initially
at rest in a stationary 45 kg boat, steps out of
the boat and onto the dock. If the boater
moves out of the boat with a velocity of 2.5
m/s to the right, what is the final velocity of
the boat?
Impulse
In a collision of two ordinary objects, both objects
are deformed, often considerably, due to the
large forces involved.
Impulse
When the collision
occurs, the force
usually
jumps from zero at the
moment of contact to
a very large value within
a very short period
of time, and then
abruptly returns to
zero again.
Impulse
From Newton’s second law, the net force
on an object is equal to the rate of change
of momentum:
F  ma 

t
Multiplying both sides by t gives:
Impulse = F x t = ρ = m x v
Impulse
Impulse helps us when dealing with forces
that occur over a short period of time.
 A golf ball being hit
A water balloon catching contest ? 
It should be noted that Impulse
I = F x t
Can be represented by the area under
a graph of force vs time.