Conservation of Energy

AP Physics 1· difficulty 4/5

rough length L k, x

A spring of constant kk is compressed by xx and launches a block of mass mm horizontally. The block then crosses a rough patch of length LL with kinetic friction coefficient μk\mu_k before reaching a smooth section. What is the block's speed after leaving the rough patch?

  • A

    v=kx2/m2μkgLv = \sqrt{kx^2/m - 2\mu_k g L}

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  • B

    v=xk/mμkgLv = x\sqrt{k/m} - \mu_k g L

  • C

    v=kx2/(2m)μkgLv = \sqrt{kx^2/(2m) - \mu_k g L}

  • D

    v=kx2/m+2μkgLv = \sqrt{kx^2/m + 2\mu_k g L}

Explanation

Energy balance: 12kx2μkmgL=12mv2\tfrac{1}{2}kx^2 - \mu_k m g L = \tfrac{1}{2}m v^2. Solving for vv gives v=kx2/m2μkgLv = \sqrt{kx^2/m - 2\mu_k g L}.

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