A cart of mass is attached to a single ideal spring of spring constant on a horizontal
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A cart of mass m is attached to a single ideal spring of spring constant k on a horizontal, frictionless track. The spring’s relaxed length corresponds to x=0. A rightward extension is defined as the positive x direction.
At a particular instant the cart is located at x=−0.12m and is moving leftward.
Assume the cart undergoes simple harmonic motion for small oscillations.
(a) Describe the direction of the restoring force acting on the cart at this instant and justify your answer in terms of the sign of the displacement.
(b) Explain whether the cart’s speed is increasing or decreasing at this instant, making explicit reference to the directions of velocity and acceleration.
(c) If the cart continues to move leftward past x=−0.12m, qualitatively sketch (label axes verbally) how the acceleration of the cart varies with position for one complete oscillation beginning at x=0 moving rightward. Indicate the sign of acceleration in each region.
(d) Provide a concise explanation of why the equilibrium position is labeled as such in the context of the net force–displacement relationship for this oscillating system.