Download AP Physics C ID

AP Physics C I.D
Systems of Particles and Linear
Momentum
“The alteration of motion is
proportional to the force
impressed” – Isaac Newton (as
related in a private
conversation to W. Evans)
What Newton means by
“motion”
p = mv
Momentum and Newton’s Second
Law Revisited
Ex. A golfer strikes a ball with a mass of 0.050 kg. The
time of impact between the golf club and the ball is 1.0
ms. If the ball leaves the face of the club with a speed
of 70.0 m/s, calculate the average force exerted on the
ball by the club.
Examples of Impulse
Impulse and F vs. t graphs
F
t
t1
t2
Ex. One legged man punts a football (mass 0.40 kg)
and gives it a launch speed of 30.0 m/s. Find the
impulse delivered to the football by the man’s foot
and average force exerted by the kicker on the ball,
if the impact time is 8.0 ms.
Ex. An 80.0 kg stuntman jumps out of a window that is 45
m above ground. a) How fast is he falling when he
reaches ground level? b) He lands on a large air
mattress, coming to rest in 1.5 s. What average force
does he experience while coming to rest? c) What force
would he experience if he landed on the ground (impact
time 10.0 ms) instead of the air mattress?
Ex. A small block of mass 0.070 kg, initially at rest,
experiences a force F for 10.0 ms. The force varies with
time as shown by the graph below. What is the final
speed of the block?
F (N)
20
t (ms)
2
6
10
Conservation of Linear
Momentum (Collisions and
Explosions)
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.
Signs of a momentum problem
• A collision occurs
• A single object “explodes” into parts
• An internal force (not external) causes
relative motion between two objects
Collisions
• Elastic: momentum is conserved, kinetic
energy is conserved
• Inelastic: momentum is conserved (if no
external forces act on the system), kinetic
energy is not conserved
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 clay 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. Ballistics Pendulum. A bullet with mass of 9.5 g
strikes a 5.4 kg wooden block of a ballistics
pendulum. The embedded bullet and block rise to a
height of 6.3 cm. What is the initial velocity of the
bullet?
Collision in two dimensions
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?
“I tossed a baseball (and a bat
for good measure) into the
air . . . .”
Center of Mass – a) the point on
an object where all the mass
can be considered to be
concentrated b) all external
forces are applied there
So, for the Second Law, the net
force causes the center of
mass to accelerate.
Center of mass for a system of
discrete objects
Ex. Two objects, one of mass m and one of mass 2m,
hang from light threads from the ends of a uniform bar
of length 3L and mass 3m. The masses m and 2m are
at distances L and 2L, respectively, shown below the
bar. Find the center of mass of the system.
3L
3m
L
2L
m
2m
Ex. (This type of problem has been on a couple of AP
MC exams) A man of mass m is standing at one of a
floating stationary barge of mass 3m. He then walks to
the other end of the barge, a distance of L meters.
Ignore frictional effects between the barge and the
water. a) How far will the barge move? b) If the man
walks with an average velocity vm, what is the velocity
of the barge vb?
Time out! A note on density
For an entire object
For a mass element