Two identical ideal springs

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

Two identical ideal springs, each with force constant

k_0 = 150\,\text{N\,m}^{-1}

, are attached in parallel between a fixed wall and a movable cart on a frictionless horizontal track. The relaxed length of each spring is the same, and both springs act simultaneously on the cart. The system is designed so that the combined springs must exert a total force of

90\,\text{N}

directed toward the wall. (a) Determine the effective force constant

k_{\text{eff}}

for the two springs acting in parallel. Briefly justify your result. (b) Calculate the magnitude of the displacement

|\Delta x|

of the cart from equilibrium required to achieve the

90\,\text{N}

total restoring force. (c) The track allows a maximum displacement of

25\,\text{cm}

before the cart reaches a bumper. Evaluate whether the required displacement from part (b) keeps the cart within the allowable range, and discuss any design implications if it does not.

Related theory

Browse the problem library