Momentum
What is momentum?
Momentum is the quantity of motion.
If an object is in motion, it has
momentum
Mass in motion
Momentum is dependent on 2 things:
– How much “stuff” is moving, Mass,
measured in kg
– How fast the stuff is moving, Velocity,
measured in m/s
Calculating Momentum
Momentum is a vector quantity.
Momentum = mass x velocity
p=mxv
An object can have a large
momentum if it has either a large
mass and/or a high speed.
Determining momentum
A small sports car and a large
delivery truck are traveling at the
same speed. Which has more
momentum?
If the car is to have the same
momentum as the truck, what about
the car must be changed?
If the truck is at rest, what is its
momentum?
Sample Problems
Determine the momentum of a ...
1) A 60-kg halfback moving eastward at 9
m/s.
Answer: 540 kg m/s east
2) A 1000-kg car moving northward at 20
m/s.
Answer: 20000 kg m/s north
3) A 40-kg freshman moving southward at 2
m/s.
Answer: 80 kg m/s south
Changing momentum
In order to change the momentum of
an object, the velocity must be
changed (if the mass remains the
same).
Any change in velocity is called
acceleration.
Newton’s second law states that any
acceleration requires a force.
Changing momentum (continued)
F = m x a (Newton’s 2nd law)
a=
v
t
F=m v
t
F t=m v
What is impulse?
F
t is called an impulse.
Impulse is a change in momentum.
Impulse is a force applied over a
time interval.
Impulse is measured in N.s.
What is the relationship between
momentum and impulse?
If two objects have the same
momentum, the same impulse is
required to change that momentum.
A large force can be applied over a
small time interval
or
A small force can be applied over a
large time interval.
Applications of Impulse
If you were to attempt to catch a
baseball with your bare hand, you
would probably move your hand
backward as you catch the ball.
Why?
How do airbags or padded
dashboards assist in protecting
drivers in a crash?
Discussion Questions
1. Would you try to stop a 150 lb (68
kg) cannonball fired towards you at
30 mph (48 km/hr)? Why not?
How does this compare with trying
to brace yourself in a car collision?
2. Show mathematically why a 36,000
kg truck traveling 0.89 m/s has the
same momentum as a 1800 kg SUV
traveling at 18 m/s.
Discussion Questions
3. During the egg throwing demonstration,
which egg experienced the greater
impulse? Which egg experienced the
greater force of impact? Which egg
experienced the greater time of impact?
4. Describe three other examples where
momentum is reduced by applying a
smaller collision force over a longer
impact time.
Practice Problem #1
A 0.50 kg football is thrown with a
velocity of 15 m/s to the right. A
stationary receiver catches the ball
and brings it to rest in 0.020 s. What
is the force exerted on the receiver?
Practice Problem #2
A 0.40 kg soccer ball approaches a player
horizontally with a velocity of 18 m/s to the
north. The player strikes the ball and causes it to
move in the opposite direction with a velocity of
22 m/s. What impulse was delivered to the ball
by the player?
Law of Conservation of Momentum
The Law of Conservation of
Momentum states that if no net force
acts on a system, the momentum of
the system cannot change.
This means that the momentum
before a collision is equal to the
momentum after a collision.
Law of Conservation of Momentum
(continued)
The equation for the law of
conservation of momentum:
pA1 + pB1 = pA2 + pB2
The momentum gained by object B is
equal to the momentum lost by
object A
Momentum is conserved if:
The system is closed (no gain or loss in
mass)
Only internal forces are involved (forces
outside the system are external forcesalthough there will always be some interaction with outside
forces they are usually small and can be ignored)
There must be collisions (the objects can
come apart or remain stuck together)
Sample Problem
A 2275 kg car going 28 m/s rear
ends a 875 kg car going 16 m/s on
ice in the same direction. The two
cars stick together. How fast does
the wreckage move immediately
after the collision?
Calculating the Answer
pA1+ pB1 = pA2 + pB2
mvA1 + mvB1 = (mA + mB)v2
(2275)(28) + (875)(16) = (2275+875)x
X = 25 m/s
Sample Problem #2
John has a mass of 200.0 kg and is
riding in a 100kg bumper car at
10.0 m/s. If he collides with Melinda
who has a mass of 25 kg and is at
rest, what is Melinda’s velocity after
the collision if John continues ahead
at a speed of 4.12 m/s after the
collision?
Calculating the Answer
pA1+ pB1 = pA2 + pB2
(300.0)(10.0) + (125)(0) = (300.0)(4.12) + (125)x
X = 14.1 m/s
Recoil Problem
An astronaut at rest in space fires a
thruster pistol that expels 35 g of
gas at 875 m/s. The combined mass
of the astronaut and pistol is 84 kg.
How fast and in what direction is the
astronaut moving after firing the
pistol?
Calculating the Answer
pA1 + pB1 = pA2 + pB2
(mA + mB)v1 = mvA + mvB
(84)(0) = (.035)(875) + (84)x
X = -.36 m/s (the direction is opposite to
that of the gas leaving the pistol)
Homework
Complete problems 7-12 on p. 210
and 13-15 on p. 214