A cart of negligible friction moves along a straight
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A cart of negligible friction moves along a straight, horizontal track from x=0 to x=9m. The net horizontal force acting on the cart varies with position as follows:
• From x=0 to 2m the force is constant at +4N.
• From x=2 to 5m the force decreases uniformly, reaching −2N at x=5m.
• From x=5 to 7m the force remains constant at −2N.
• From x=7 to 9m the force increases uniformly to 0N at x=9m.
Assume the +x direction is to the right and that the cart moves only in that direction throughout the motion.
(a) Identify the interval(s) in which the force does positive work on the cart and the interval(s) in which the force does negative work. Justify your answer in terms of the sign of the force and the direction of the displacement.
(b) Without performing numerical calculations, rank the four intervals listed in the stimulus from greatest magnitude of work done on the cart to least magnitude of work done. Provide reasoning based on the qualitative areas under the force–position graph.
(c) The cart is released from rest at x=0. Describe qualitatively how the cart’s speed changes as it travels through each of the four intervals. Explain your reasoning in terms of energy transfer.