Physics

Physics

Problem

A block attached to a horizontal spring oscillates between x=−Ax = -A and x=+Ax = +A. When the block is at x=13Ax = \tfrac{1}{3}A, which comparison between its kinetic energy KK and potential energy UU is most accurate? a) K=UK = U b) KK is greater than UU c) UU is greater than KK d) K=2UK = 2U
Intuitive explanation

The key is recognizing that total mechanical energy in a spring system is conserved and splits between kinetic and potential forms. At any position xx, the potential energy is U=12kx2U = \tfrac{1}{2}kx^2, which depends on how far you are from equilibrium—not on how fast you're moving. When the block is only one-third of the way to maximum displacement, it's still relatively close to equilibrium where the spring force is weak, so potential energy is small and most of the total energy remains kinetic.

Intuitive explanation

The key is recognizing that total mechanical energy in a spring system is conserved and splits between kinetic and potential forms. At any position xx, the potential energy is U=12kx2U = \tfrac{1}{2}kx^2, which depends on how far you are from equilibrium—not on how fast you're moving. When the block is only one-third of the way to maximum displacement, it's still relatively close to equilibrium where the spring force is weak, so potential energy is small and most of the total energy remains kinetic.

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