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 big truck and a roller skate
moving down the street at the same
speed. The considerably greater mass
of the big truck gives it a considerably
greater momentum. If the big 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.
p = 540 kg*m/s, east
b.) 1000 kg car moving northward at 20 m/s.
p = 20,000 kg*m/s, north
c.) 40 kg man moving southward at 2 m/s.
p = 80 kg*m/s, south
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 p = 40,000 units
b.) its mass were doubled p = 40,000 units
c.) both its velocity and mass were
doubled p = 80,000 units
If the boulder and the boy
have the same momentum,
will the boulder crush the
boy?
Hint: think about the
momentum formula!
p = mv
DEMONSTRATIONS
• Egg and the Blanket
IMPULSE – A force applied for a
period of time which results in a
change of momentum.
Impulse = change in momentum
F∆t = ∆p = ∆(mv)
F∆t = mvf - mvi
F∆t = m (vf – vi)
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.
The Wall
The Haystack
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
Greatest Impulse?
Therefore, a larger Force
and impulse occurs!
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
-720 kg*m/s
(b) the average force exerted on him by the
-240 N
snow bank
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 Cradle
Firecracker
both sides gain momentum
net momenta = zero
momentum is conserved
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!!!
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
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?
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
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
inelastic
elastic
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 big truck and a Volkswagen have
a head-on collision. Which vehicle
will experience the greatest force
of impact?
a.) Big truck
b.) Volkswagon
c.) impossible to figure out
d.) same