A student investigates the restoring force acting on a pendulum bob during…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A student investigates the restoring force acting on a 0.10kg pendulum bob during small‐angle oscillations. Using a sensitive force probe, they measure the horizontal component of the string tension (equal in magnitude to the tangential restoring force) for several small linear displacements of the bob from equilibrium. The data are recorded in the table below.
Linear displacement x (cm) 1.0 2.0 3.0 4.0
Restoring force F (N) 0.020 0.039 0.060 0.079
(1) Plot (or conceptually sketch) F versus x and determine the numerical value of the slope k of the best-fit line through the data. Include appropriate units in your answer.
(2) Using the slope found in part (a), calculate the length L of the pendulum implied by the data. Show all steps clearly.
(3) A direct measurement with a meter stick gives L=0.52m. Compute the percent difference between this measured value and the value obtained in part (b) and comment on possible experimental sources of discrepancy.
(4) For the largest displacement listed in the table, determine the corresponding angular displacement of the bob in degrees.