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Momentum
• All objects have mass; so if an object is
moving, then it has momentum - it has
its mass in motion.
• The amount of momentum which an
object has is dependent upon two
variables:
– how much matter is moving?
– how fast the matter is moving?
• Momentum: "mass in motion”
• Equation: p = m x v
• Unit: kg*m/s
Momentum
• Momentum is a vector quantity.
Momentum
Consider a Mack truck and a roller
skate moving down the street at the
same speed. The considerably greater
mass of the Mack truck gives it a
considerably greater momentum. If the
Mack truck were at rest, which would
have the greater momentum?
If an object is at rest, the momentum of that
object is “0” because there is no mass in
motion.
Momentum Questions
1. Determine the momentum of a ...
a.) 60 kg halfback moving eastward at 9 m/s.
b.) 1000 kg car moving northward at 20 m/s.
c.) 40 kg man moving southward at 2 m/s.
Momentum Questions
2. A car possesses 20,000 units of
momentum. What would be the
car's new momentum if ...
a.) its velocity were doubled
b.) its mass were doubled
c.) both its velocity and mass were
doubled
If the boulder and the boy
have the same momentum,
will the boulder crush the
boy?
Hint: think about the
momentum formula!
p = mv
Impulse
• The impulse experienced by an object is
the force•time.
• The momentum change of an object is the
mass•velocity change.
• The impulse equals the momentum
change.
Impulse
Force x time = mass x change in velocity
F * t = m * Δv
Impulse = Change in Momentum
N * sec = kg * m/s
IMPULSE – A force applied for a
period of time which results in a
change of momentum.
Impulse = change in momentum
To change the momentum of a body, a
force must be applied to the mass. The
longer this force is applied to the mass, the
greater effect it will have on changing the
momentum.
Impulse
• A change in momentum in a short
time requires a large force.
• A change in momentum in a long time
requires a small force.
1. An 80 kg skier loses control and
demolishes a snow bank. If it takes the
skier 3 seconds to come to rest from an
impact speed of 9 m/s, find:
(a) the impulse on the man
(b) the average force exerted on him by the
snow bank
To change momentum, exert an impulse on it.
An outside push or pull is required to change
momentum.
Hey!
It’s the
Law!
The momentum
of a system
remains the same
unless acted
upon by an
external force.
Can you think of any
examples where you think
momentum is conserved?
Shooting Pool
Newton’s Balls
Firecracker
both sides gain momentum
net momenta = zero
momentum is conserved
Conservation of Momentum
What happens to the speed of a
fighter aircraft chasing another when
it opens fire? What happens to the
speed of the pursued aircraft when it
returns the fire (from the rear guns)?
Bored Astronauts
Suppose there are 3 astronauts outside
a spaceship. Two of them decide to
play catch. All the astronauts weigh the
same and are equally strong. The game
begins with the first astronaut throwing
the second astronaut to the third. How
long will the game last?
Σ(m1v1) i= Σ(m2v2)f
m1v1i + m2v2i = m1v1f + m2v2f
Watch out for negatives!!!
Tennis and Cannon Activity
• Conservation of Momentumexplosion interaction
• pi = pf
• m1v1i + m2v2i = m1v1f + m2v2f
Find the velocity of the rifle.
-0.75 m/s
Follow-up Question: Would you want to fire a rifle
that has a bullet ten times as massive as the rifle?
Explain.
Three Types of Interactions
1. Bouncy Interaction – two objects collide
and bounce off each other. No permanent
deforming damage.
m1v1i + m2v2i = m1v1f + m2v2f
2. Sticky Interaction – two objects collide and
stick together. Final velocities are the same.
m1v1i + m2v2i = (m1 + m2)vf
2. Explosion Interaction – two objects explode
and move apart from each other.
m1v1i + m2v2i = m1v1f + m2v2f
The Next Michelle Kwan…?
A softball player wishes to determine
her mass. She glides without friction
along on some ice skates at 1.5 m/s,
and throws a ball of 0.8 kg mass at 27
m/s. She then determines that she has
slowed to 1.2 m/s. What is her mass?
Ans: m = 68 kg
Momentum Railroad Problem of Doom
A 500 kg railroad car moving at a speed
of 30 m/s collides and sticks together
with a 1000 kg railroad car initially at
rest. What will be the resulting speed of
the cars after the collision?
Sample Problem
A truck and a car collide
head on. The speed of the
truck was 20 m/s, and that
of the car was 30 m/s. The
truck has a mass of 5 times
that of the car. If they stick
together after the collision,
how fast are they moving,
as a unit, just after the
collision?
The Power of Cheese Salami!
A 30 g bullet traveling at 300 m/s
rips through a 0.65 kg salami and
exits at 236 m/s.
How fast does the salami move after
the bullet leaves?
More Momentum
If a Mack truck and a Volkswagen
have a head-on collision, which
vehicle will experience the greatest
force of impact? The greatest
impulse? The greatest change in
momentum? The greatest
acceleration?
Find the impulse for the following graph.
60
50
40
F (N)
30
20
10
2
4
6
8 10 12 14 16 18 20 22
t (s)
Conservation of Momentum
A golf ball is moving with 1 kgm/s and bounces of a
bowling ball initially at rest; after the collision, what is
the momentum of the bowling ball?
Conservation of Momentum
Farmer Joe shoots a bullet of
mass 4 g from a gun of mass
7 kg with a speed of 1420 m/s
at his collection of coke cans.
What is the speed with which
the gun recoils?
Answer: V = -0.811 m/s
Net ∆mv (before collision) = Net ∆mv (after collision)
The total momentum before
a collision is equal to the total
momentum after a collision –
Conservation of Momentum
Inelastic Collision:
If the mass of each railroad car is the
same, determine the velocity after the
collision.
m/s
m/s
5 m/s
You guessed it… MOMENTUM
Would a head-on collision between
two cars be more damaging to the
occupants if the cars stick together
or if the cars rebound upon
impact?
inelastic
elastic
Sailing, Sailing..
Gilligan’s super escape ice sail craft is stalled on
a frozen lake on a windless day. His only piece of
auxiliary equipment is a large fan that blows air
into the sail. If all the wind produced by the fan
strikes and bounces backward from the sail, the
craft will move:
•
•
•
Backward
Forward
Not at all
Review
You jump off a table. When you land on the
floor you bend your knees in order to…
a.) Decrease the impulse on you by the floor
b.) Decrease the force applied to you by the
floor
c.) Increase the time it takes to stop
d.) Both a and b
e.) Both b and c
f. ) All of the above
Review
A Mack truck and a Volkswagen
have a head-on collision. Which
vehicle will experience the greatest
force of impact?
a.) Mack truck
b.) Volkswagon
c.) impossible to figure out
d.) same
Find the impulse for the following graph.
60
50
40
F (N)
30
20
10
2
4
6
8 10 12 14 16 18 20 22
t (s)