A student attempts to measure the local gravitational field strength by timing…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A student attempts to measure the local gravitational field strength by timing oscillations of a simple pendulum. The pendulum length, measured from the pivot to the center of mass of the bob, is 0.993m±0.005m. Using a stopwatch, the student records a time of 200.0s for 100 complete oscillations.
(a) Derive an expression for g in terms of the measured length l and the oscillation period T for small-angle motion.
(b) Using the experimental data, calculate the student’s value of g. Include appropriate units.
(c) Determine the percent difference between the student’s value and the accepted standard 9.81m/s2.
(d) Using the stated uncertainty in the length measurement, estimate the percent uncertainty in the calculated value of g. Indicate whether the accepted value lies within the experimental uncertainty and justify your conclusion.