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AP Physics I.D
Impulse and Momentum
The Hummer and the Smart Car
Another look at the Second Law
“The alteration of motion is
proportional to the force
impressed” – Isaac Newton (as
related in a private conversation to
W. Evans)
Momentum
• Product of mass and velocity
• It’s a vector Victor
p = mv
Impulse (a vector and has same
direction as average force)
So you can see, a large force
acting for a short period of time
can create the same change in
momentum as a small force
acting for a large period of time.
Examples of impulse
• Two AP science teachers vs. a doubles team
headed for state
• Daniel Sepulveda
• Bunting a baseball
• Dick Fosbury
• Air bags
• Bending your knees
• Boxing
• An egg and sheet
Ex. A 80.0 kg stuntman jumps out of a window that 45 m
above the ground. a) How fast is he falling when he reaches
ground level? b) He lands on a large, air filled target, coming
to rest in 1.5 s. What average force does he experience while
coming to rest? c) What if he had landed on the ground
instead, coming to rest in 10.0 ms? (ouch!)
Ex. An object with mass 3m moves along the +x-axis with a
speed v. A second object with mass 2m and speed 2v moves
along the –y-axis with a speed of 2v. What is the magnitude of
the net momentum of the two objects?
Graphing force vs. time
Conservation of Linear
Momentum
Two types of forces on the
system
• Internal – forces that objects within the
system exert on each other
• External – forces that objects outside the
system exert on each other
Linear momentum is conserved
if the sum of the external forces
is zero and the system is
isolated. The momentum before
the event is equal to the
momentum after the event.
Ex. An astronaut is floating in space near her shuttle when she
realizes that the cord that attaches her to the ship has become
disconnected. Her total mass (body, suit and equipment) is
91 kg. She reaches into her pocket, finds a 1.0 kg metal tool,
and throws it directly away from the ship with a speed of 9.0
m/s. If the ship is 10.0 m away, how long will it take her to
reach it?
Rifle Recoil: Find the recoil velocity of a 5.0 kg rifle that shoots
a 0.050 kg bullet at a speed of 120 m/s.
Collisions (and explosions) in
One Dimension
Elastic collision – momentum and
kinetic energy are conserved
(objects bounce off one another –
in real life this only happens at the
atomic level)
Inelastic collision – momentum is
conserved, but kinetic energy is
not
Completely inelastic collision –
all kinetic energy converted to
other forms of energy – the
objects stick together (thud)
Note: momentum is conserved if no
external forces act on the system, but
kinetic energy is conserved only in
elastic collisions.
Ex. Two balls roll toward each other. The red ball has mass of
0.50 kg and a speed of 4.0 m/s just before impact. The green ball
has a mass of 0.20 kg and a speed of 2.0 m/s. After the head-on
collision, the red ball continues in its initial direction with a speed
of 2.0 m/s. Find the velocity of the green ball after the collision. Is
the collision elastic or inelastic?
Ex. Two blobs of clay are thrown towards each other and
collide in mid-air. The red clay has a mass of 0.50 kg and a
speed of 4.0 m/s just before impact. The green ball has a
mass of 0.30 kg and a speed of 2.0 m/s. If the collision is
completely inelastic, determine the velocity of the composite
object immediately after the collision.
Ex. A bullet with a mass of 0.0100 kg strikes, and is
embedded in a block (mass of 2.50 kg) that is suspended by a
thin cord. The block rises a vertical height of 0.650 m because
of the collision. What is the initial velocity of the bullet?
Collision in Two Dimensions
If no external forces act on a system,
horizontal and vertical components of
momentum are conserved.
Ex. A 500 kg car travels at 20.0 m/s due north. It collides
with a 500 kg traveling due west at 30.0 m/s. The cars lock
bumpers and stick together. What is the velocity of the
combined cars immediately after impact?
Ex. An object of mass m moves with velocity v toward
stationary object of mass 2m. After impact, the objects move
off in directions as shown. a) Determine the magnitudes of the
velocities after the collisions in terms of v. b) Is this an elastic
or inelastic collision?