A cart moves along a straight track while a horizontal external force acts on it
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A cart moves along a straight track while a horizontal external force acts on it. The component of the force parallel to the track varies with the cart’s position x as follows:
• From x = 0 m to x = 2 m, the force is constant at +4 N.
• From x = 2 m to x = 4 m, the force decreases linearly to 0 N at x = 4 m.
• From x = 4 m to x = 6 m, the force is constant at –3 N.
Take +x to be the direction of increasing position.
(1) Sketch the force-versus-position graph implied by the description, labeling all key values.
(2) Calculate the numerical value of the work done by the force on the cart over the entire displacement from x = 0 m to x = 6 m. Clearly indicate the contribution of each segment and the overall sign.
(3) Interpret physically what the sign of the total work indicates about energy transfer to or from the cart during this 6 m interval.