AP Free Response Question
2000 C1
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You are conducting an experiment to measure the acceleration due to gravity,
g
_{u}
, at an unknown location. In the measurement apparatus, a simple pendulum swings past a photogate located at the pendulum's lowest point, which records the time t
_{10}
for the pendulum to undergo 10 full oscillations. The pendulum consists of a sphere of mass
m
at the end of a string and has a length
. There are four versions of this apparatus, each with a different length. All four are at the same unknown location and the data shown below are sent to you during the experiment.
(a) For each pendulum, calculate the period
T
and the square of the period. Use a reasonable number of significant figures. Enter these results in the table above.
(b) On the axes below, plot the square of the period versus the length of the pendulum. Draw a best fit straight line for this data.
(c) Assuming that each pendulum undergoes small amplitude oscillations, from your fit determine the experimental value
g
_{exp}
of the acceleration due to gravity at this unknown location. Justify your answer.
(d) If the measurement apparatus allows a determination of
g
_{u}
that is accurate to within 4%, is your experimental value in agreement with the value 9.80 m/s
^{2}
? Justify your answer.
(e) Someone informs you that the experimental apparatus is in fact near Earth's surface, but that the experiment has been conducted inside an elevator with a constant acceleration
a
. Assuming that your experimental value
g
is exact, determine the magnitude and direction of the elevator's acceleration.
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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Sample NY Regents Review Questions
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