A small puck of negligible height slides without friction along a straight horizontal…
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A small puck of negligible height slides without friction along a straight horizontal air track. The puck is connected on its left side to spring A (spring constant kA=80N/m) and on its right side to spring B (spring constant kB=120N/m). Both springs are attached to fixed walls, so the puck is constrained to move only along the x-axis between the springs.
The coordinate axis is chosen with origin at the system’s equilibrium position, with positive x to the right.
(a) For a puck displacement x=+0.06m, determine the individual forces exerted on the puck by springs A and B, specifying the direction and algebraic sign of each.
(b) Repeat part (a) for a displacement x=−0.06m.
(c) Using your qualitative results from parts (a) and (b) and appropriate numerical reasoning, construct a piecewise algebraic expression for the net spring force Fnet(x) acting on the puck for any small displacement x about equilibrium. Be sure to indicate clearly which expression applies for x>0 and which applies for x<0.
(d) On blank axes of your own, sketch the graph of Fnet(x) versus x for displacements in the range −0.10m≤x≤+0.10m. Label key points, slopes, and intercepts, and explain how the graph illustrates the restoring nature of the combined spring system.