AP Free Response Question
2003 C2
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An ideal spring is hung from the ceiling and a pan of mass
M
is suspended from the end of the spring, stretching it a distance
D
as shown above. A piece of clay, also of mass
M
, is then dropped from a height
H
onto the pan and sticks to it. Express all algebraic answers in terms of the given quantities and fundamental constants.
Determine the speed of the clay at the instant it hits the pan.
Determine the speed of the pan just after the clay strikes it.
Determine the period of the simple harmonic motion that ensues.
Determine the distance the spring is stretched (from its initial unstretched length) at the moment the speed of the pan is a maximum. Justify your answer.
The clay is now removed from the pan and the pan is returned to equilibrium at the end of the spring. A rubber ball, also of mass
M
, is dropped from the same height
H
onto the pan, and after the collision is caught in midair before hitting anything else.
Indicate below whether the period of the resulting simple harmonic motion of the pan is greater than, less than, or the same as it was in part (c).
_______Greater than _______Less than _______The same as
Justify your answer.
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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