AP Free Response Question
2002 C2
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The cart shown above is made of a block of mass
m
and four solid rubber tires each of mass
m/4
and radius
r
. Each tire may be considered to be a disk.
NOTE: A disk has rotational inertia
where
M
is the mass and
L
is the radius of the disk.
The cart is released from rest and rolls without slipping from the top of an inclined plane of height
h
. Express all algebraic answers in terms of the given quantities and fundamental constants.
Determine the total rotational inertial of all four tires.
Determine the speed of the cart when it reaches the bottom of the incline.
After rolling down the incline and across the horizontal surface, the cart collides with a bumper of negligible mass attached to an ideal spring, which has a spring constant
k
. Determine the distance
x
_{m}
the spring is compressed before the cart and bumper comes to rest.
Now assume that the bumper has a non negligible mass. After the collision with the bumper, the spring is compressed to a maximum distance of about 90% of the value of x
_{m}
in part (c). Give a reasonable explanation for this decrease.
Topic Formulas
Description
Published Formula
angular displacement
angular momentum
angular velocity
center of mass
centripetal acceleration
friction
gravitational force (vector)
gravitational potential energy
Hooke's Law
impulse
kinetic energy
linear momentum
linear velocity and angular velocity
moment of inertia
net torque
Newton's 2nd Law
Newton's Law of Universal Gravitation
period and frequency
period of a simple pendulum
period of a spring
potential elastic energy
potential energy
power (dot product)
rate of change of momentum
rate of change of work
rotational kinetic energy
torque
uniform acceleration  displacement and instantaneous velocity
uniform acceleration  instantaneous position
uniform acceleration  instantaneous velocity
work (dot product)
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