A particle of mass m is suspended from the roof of a car by a light spring of force constant k. The car accelerates horizontally with constant acceleration a. After transients die out, the spring extension is:
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Question

A particle of mass m is suspended from the roof of a car by a light spring of force constant k. The car accelerates horizontally with constant acceleration a. After transients die out, the spring extension is:

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G1 Physics · Accepted Answer

In the car frame, the particle is in equilibrium under gravity mg downward, pseudo force ma horizontally opposite the car acceleration, and spring tension. The spring tension magnitude is the resultant T = m√(g²+a²). Since T=kx, the extension is x = m√(g²+a²)/k.