PhysicsLAB 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.

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