A physics student investigates why a grandfather clock that kept accurate time at sea…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A physics student investigates why a grandfather clock that kept accurate time at sea level now runs noticeably slower in a mountain cabin. The student notes that the pendulum length was not altered during transport. Assume the pendulum always swings with a small angular displacement.
(a) Describe qualitatively how the period of a simple pendulum depends on its length and on the local value of the gravitational field strength. Use verbal reasoning; do not perform any calculations.
(b) Suppose the clockmaker wishes to explore the relationship between the square of the measured period T2 and the pendulum length l. Describe the shape and key features of a graph of T2 versus l that the student should expect for small-angle oscillations.
(c) Explain why data points collected at initial displacements larger than 15∘ would tend to lie above the ideal curve you described in part (b).
(d) The student discovers that the mountain-top value of g is about 0.3% smaller than at sea level. Explain, without calculation, whether the clock would gain or lose time each day if its length is left unchanged, and account for the observed behavior mentioned in the prompt.