A cart of mass is free to move on a frictionless horizontal track
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A cart of mass 1.2kg is free to move on a frictionless horizontal track. Two identical springs, each with constant k=90N/m, are attached to fixed supports on opposite sides so that the cart is positioned between them. The equilibrium position of the cart is x=0. A coordinate axis is defined so that rightward displacements are positive.
The cart is initially pushed 0.12m to the right and released from rest.
(a) While the cart is held at x=+0.12m (just before release), determine the direction and sign (positive or negative) of the force exerted on the cart by the right-hand spring. Explain your reasoning.
(b) At the same position, determine the direction and sign of the force exerted by the left-hand spring. Explain your reasoning.
(c) Calculate the net spring force (magnitude and sign) acting on the cart at x=+0.12m. Show how the individual contributions combine to give the net result, including the sign.
(d) Using the net force from part (c), compute the cart’s initial acceleration immediately after it is released. Indicate the direction of this acceleration with respect to the positive axis.