A team of students investigates how the period of a pendulum depends on its length
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A team of students investigates how the period of a pendulum depends on its length. They collect the data shown below, each period value representing the average of 10 oscillations. The amplitude never exceeds 5∘. Air resistance is negligible.
Length l (m): 0.20, 0.40, 0.60, 0.80, 1.00
Average period T (s): 0.90, 1.27, 1.55, 1.80, 2.01
(a) Explain how the students could transform these data so that a plot of the transformed variables yields a straight line whose slope can be used to determine g. Specify both variables that would be plotted on the horizontal and vertical axes.
(b) Using the transformed variables you identified in part (a), calculate the numerical value of the slope based on the given data. Show work.
(c) From the slope obtained in part (b), compute a value for the local gravitational field strength g. Include units.
(d) The stop-watch used has a reaction-time uncertainty equivalent to ±0.05s on any single timing of 10 oscillations. Estimate the percent uncertainty in the value of g you obtained and comment on the reliability of the experiment.