AP Free Response Question
2007 C3
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The apparatus above is used to study conservation of mechanical energy. A spring of force constant 40 N/m is held horizontal over a horizontal air track, with one end attached to the air track. A light string is attached to the other end of the spring and connects it to a glider of mass
m
. The glider is pulled to stretch the spring an amount
x
from equilibrium and then released. Before reaching the photogate, the glider attains its maximum speed and the string becomes slack. The photogate measures the time
t
that it takes the small block on top of the glider to pass through. Information about the distance
x
and the speed
v
of the glider as it passes through the photogate are given below.
(a) Assuming no energy is lost, write the equation for conservation of mechanical energy that would apply to this situation.
(b) On the grid below, plot
v
^{2}
versus x
^{2}
. Label the axes, including units and scale.
(c) Graph Analysis
i. Draw a bestfit straight line through the data.
ii. Use the bestfit line to obtain the mass
m
of the glider.
(d) The track is now tilted at an angle
as shown below. When the spring is unstretched, the center of the glider is a height
h
above the photogate. The experiment is repeated with a variety of values of
x
.
i. Assuming no energy is lost, write the new equation for conservation of mechanical energy that would apply to this situation.
ii. Will the graph of
v
^{2}
versus x
^{2}
for this new experiment be a straight line? 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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