Linear Momentum
• why is more force needed to stop a
train than a car if both travel at the
same speed?
• why does a little tiny bullet have so
much force on impact?
• how do you steer a satellite or
shuttle in space?
Momentum (p) a term which describes the
product of mass and velocity
• changing momentum depends upon changing
either mass or velocity
• the train is harder to stop than the car
because its larger mass means a greater
change in momentum
• a bullet has a tremendous impact because
its change in speed upon impact is extremely
large- hence a large change in momentum
Momentum depends directly upon mass and
directly upon velocity:
p = mv
units:
kg • m/s
A change in momentum usually means a
change in velocity.
A change in momentum will only occur if a
force acts upon the object and changes its
velocity (it accelerates the object!)
F = ma
= m∆v
∆t
therefore:
F∆t = m∆v
Impulse
produces
a change in
momentum
In order to change the momentum of an object, a
force must be exerted on it for a given period of
time!
A 1400 kg car traveling in the positive direction
takes 10.5 seconds to slow from 25.0 meters per
second to 12.0 meters per second. What is the
average force on the car during this time?
A cue stick applies an average force of 66 N to a
stationary 0.17 kg cue ball for 0.0012 s. What is the
magnitude of the impulse on the cue ball?
A government agency estimated that air bags
have saved over 14,000 lives as of April 2004 in
the United States. (They also stated that air bags
have been confirmed as killing 242 people, and
they stress that seat belts are estimated to save
11,000 lives a year.) Assume that a car crashes
and has come to a stop when the air bag inflates,
causing a 75.0 kg person moving forward at 15.0
m/s to stop moving in 0.0250 seconds. (a) What is
the magnitude of the person's impulse? (b) What
is the magnitude of the average force the airbag
exerts on the person?
Law of Conservation of Momentum
the total (vector sum) momentum of two (or
more) objects before a collision will be the
same as after the collision!
*a collision simply means a force acted
over a relatively short period of time!
 an explosion would be a collision!
There are two types of collisions:
• Inelastic- kinetic energy is not conserved
• Elastic- kinetic energy is conserved
A 1.20 kg cart heading east at .50 m/s collides
head on with a 1.60 kg cart heading west at .70
m/s and they lock together. What is the velocity
of the two carts afterward?
pbefore = pafter
m1 = 1.20 kg
m1v1 + m2v2 = (m1 + m2)v
v1 = .50 m/s
(1.20 kg)(.50 m/s)+(1.60 kg)(-.70 m/s)
m2 = 1.60 kg
= (1.20 kg + 1.60 kg)v
v2 = -.70 m/s
.60 + (-1.12) = 2.80v
v=?
v = -.19 m/s
Is this collision
or
elastic?
.19 m/s West
An 6.00 kg bowling ball traveling at 2.00 m/s
collides with an 8.00 kg ball that is at rest. After
the collision, the 6.00 kg ball is reduced in speed to
.500 m/s. What is the speed of the other ball after?
p = p’
m1 = 6.00 kg
v1 = 2.00 m/s
m1v1 + m2v2 = m1v1 + m2v2
m2 = 8.00 kg (6.00 kg)(2.00 m/s) + 0 =
v2 = 0
(6.00 kg)(.500 m/s) +(8.00 kg)(v2)
v1 = .500 m/s
v2 = 12.0 - 3.00
=1.13 m/s
v2= ?
Elastic?
8.00
A car of 1200 kg heading east at 25.0 m/s collides
with a second car of 1800 kg that is heading north
at 21.0 m/s. The cars stick together after the
collision. What is the velocity of the cars after the
collision?
Remember that momentum is a vector
and is conserved in both x and y
directions!
A little red wagon with a mass of 75.0 kg is
rolling along when a 210.0 kg mail sack is
dropped into the wagon. The wagon and the mail
sack continue to roll along at 1.37 m/s. What
was the speed of the little red wagon before the
mail sack was dropped on it?
A bowling ball of mass 6.0 kg is traveling at 4.0
m/s when it collides with an 8.0 kg ball. After
the collision, the second ball accelerates to 4.75
m/s and the first is traveling 1.0 m/s opposite of
its initial direction. What was the velocity of the
second ball initially?
Is the previous collision an elastic or inelastic
collision?
While on a space walk, a 75.0 kg astronaut,
initially at rest relative to the shuttle, throws a
hammer with a speed of 4.00 m/s. If the mass of
the hammer is 3.00 kg, what is the resulting
velocity of the astronaut?
A second astronaut, mass 85.5 kg, initially at rest,
catches the thrown hammer. What is his resultant
velocity?
A .300 kg dynamics cart traveling at .650 m/s
collides with a second, identical cart at rest. They
stick together after the collision. Find their
velocity after and find how much kinetic energy
was lost during the collision.
An 86.0 kg running back heading north at 9.00
m/s is hit head on by a 92.0 kg linebacker going
south at 6.00 m/s. Assume the linebacker wraps
up well and find their velocity immediately after
they collide.
A 925 kg car traveling straight east at 24.0 m/s is
broad-sided by a pick up truck of mass 1250 kg
traveling north at 15.5 m/s. After the collision,
the car has a velocity of 19.5 m/s at 18.0˚ East of
North. What is the velocity of the truck after the
collision?