AP Free Response Question
2008 C3
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In an experiment to determine the spring constant of an elastic cord of length 0.60 meters, a student hangs the cord from a rod as represented above and then attaches a variety of weights to the cord. For each weight, the student allows the weight to hang in equilibrium and then measures the entire length of the cord. The data are recorded in the table below:
(a) Use the data to plot a graph of weight versus length on the axes below. Sketch a best-fit straight line through the data.
(b) Use the best-fit line you sketched in part (a) to determine an experimental value for the spring constant
k
of the cord.
The student now attaches an object of unknown mass
m
to the cord and holds the object adjacent to the point at which the top of the cord is tied to the rod, as represented below. When the object is released from rest, it falls 1.5 m before stopping and turning around. Assume that air resistance is negligible.
(c) Calculate the value of the unknown mass
m
of the object.
(d) i. Calculate how far down the object has fallen at the moment it attains its maximum speed.
(d) ii. Explain why this is the point at which the object has its maximum speed.
(d) iii. Calculate the maximum speed of the object.
Topic Formulas
Description
Published Formula
angular displacement
angular momentum
angular velocity
center of mass
centripetal acceleration
centripetal acceleration
elastic potential energy
friction
gravitational force (vector)
gravitational potential energy
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 energy
power
power
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
work (dot product)
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