Download Kinematics Multiples

Momentum Concepts
From Old AP’s
1. Two pucks are attached by a stretched spring and are initially at rest on a frictionless
surface, as shown above. The pucks are then released simultaneously. If puck I has three
times the mass of puck II, which of the following quantities is the same for both pucks as
the spring pulls the pucks toward each other?
a. Speed.
b. Velocity.
c. Acceleration.
d. Kinetic energy.
e. Magnitude of momentum.
* E. Since there are no outside forces (the spring is an internal force), momentum is
conserved. Since the pucks began at rest, the momentum of the system is zero—which
means the pucks must have equal and opposite momentum.
2. Which of the following is true when an object of mass m moving on a horizontal
frictionless surface hits and sticks to an object of mass M > m, which is initially at rest on
the surface?
a. The collision is elastic.
b. All of the initial KE of the less massive object is lost.
c. The momentum of the objects that are stuck together has a smaller magnitude
than the initial momentum of the less-massive object.
d. The speed of the objects that are stuck together will be less than the initial
speed of the less-massive object.
e. The direction of motion of the objects that are stuck together depends on
whether the hit is a head-on collision.
* D. Because momentum is conserved, if mass increases, then speed must decrease.
Questions 3 and 4:
A ball of mass m is dropped from rest from a height H above the ground and bounces
back to its original height after a perfectly elastic collision with a metal plate on the
ground.
3. Which of the following velocity vs. time graphs best represent the motion of the ball?
* D. This one can be a little tricky because we usually draw graphs in free fall. What we
have here is two periods of free fall with a collision in between. The graphs don’t actually
depict the change in velocity during the collision—it would be a very steep line. You
want the graph where the ball’s velocity is increasing at a uniform rate and is negative as
it approaches the floor. Where the graph shows an asymptote it should show a steep
incline headed back to max positive velocity which linearly decreases as it reaches the
top turnaround. This graph is counter-intuitive because we are used to visualizing the
motion of the object and not its velocity.
4. Which of the following graphs best represents the KE and gravitational PE functions
vs. time for the ball?
*A
The KE is a max. when the ball impacts the floor and then decreases—which rules out
graphs C and E.
Although the speed varies linearly with time, KE is the square of the speed, so it should
be a parabola, which rules out graph B.
In graph D the PE is decreasing quickly at first and then more slowly while in graph A
the PE is decreasing slowly then quickly. Since the ball speeds up as it approaches the
floor, the rate of change of PE is increasing. (it is changing height more quickly as it
approaches the floor).
5. Two objects move toward each other, collide and separate. If there was no net
external force acting on the objects, but some kinetic energy was lost, then:
a. the collision was elastic and total linear momentum was conserved.
b. the collision was elastic and total linear momentum was NOT conserved.
c. the collision was NOT elastic and total linear momentum was conserved.
d. the collision was NOT elastic and total linear momentum was not conserved.
e. none of the above.
* C. No external forces means momentum was conserved. Energy lost means the
collision was not elastic.
6. A heavy cue ball collides with a lighter eight ball at rest. Both balls continue in the
forward direction after the crash. The eight ball speeds up and the cue ball slows down.
Which of the following is/are true?
I. The momentum lost by the cue ball is gained by the eight ball.
II. The energy lost by the cue ball is gained by the eight ball.
a. Only I is true.
b. Only II is true.
c. I and II are both true.
d. I and II are both false.
* A. By conservation of momentum (neglecting the external force of the felt on the
table), the momentum lost by the cue ball has been transferred to the eight ball.
However, unless the collision is perfectly elastic, there is energy lost to sound,
deformation, etc. These forces must be internal (molecular) forces and not friction from
the outside or momentum would not be conserved.
7.
(2004B, 85%)
How does an air mattress protect a stunt person landing on the ground after a stunt?
a. It reduces the kinetic energy loss of the stunt person.
b. It reduces the momentum change of the stunt person.
c. It increases the momentum change of the stunt person.
d. It shortens the stopping time of the stunt person and increases the force applied during
the landing.
e. It lengthens the stopping time of the stunt person and reduces the force applied during
the landing.
*E.
The change in momentum of the stunt person is pre-determined. His momentum goes
from mass * velocity to zero, no matter what he lands on. Remember the
impulse/momentum relationship: F* t = m * (Vf - Vi). If you solve for force:
F = m (Vf - Vi)/t, so the greater the time, the lesser the force.