PhysicsLAB: 2000 C1

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 t₁₀ 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/s²? 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.

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