A student jogs at constant speed around a circular track marked with evenly spaced…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A student jogs at constant speed around a circular track marked with evenly spaced lane lines. The innermost lane has a radius of 18 m, while the next lane out has a radius of 20 m.
Assume each jogger maintains exactly the same constant tangential speed of 4.5 m s⁻¹ in their respective lane.
(a) Describe the direction of the acceleration experienced by a jogger running in uniform circular motion and explain why that direction is required for the motion to remain circular.
(b) Without performing a numerical calculation, explain qualitatively how the magnitude of the required acceleration for a jogger changes when the radius of the circular path increases while the speed remains the same.
(c) Using proportional reasoning, compare the magnitudes of the accelerations of the two joggers in the 18 m and 20 m lanes. State which jogger experiences the larger acceleration and justify your answer.
(d) If both joggers suddenly move to an outer lane with radius 25 m but continue to run at 4.5 m s⁻¹, describe how the change affects the net horizontal force each jogger’s legs must provide. Explain your reasoning in terms of the relationship between force and acceleration.