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Conservation of Energy

AP Physics 1· difficulty 3/5

A spring (k=500 N/mk = 500~\text{N/m}) is compressed 0.20 m0.20~\text{m} against a 0.50 kg0.50~\text{kg} block on a frictionless surface, then released. What launch speed does the block reach?

  • A

    2.0 m/s2.0~\text{m/s}

  • B

    4.0 m/s4.0~\text{m/s}

  • C

    10 m/s10~\text{m/s}

  • D

    6.3 m/s6.3~\text{m/s}

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Explanation

12kx2=12mv2⇒v=xk/m=0.20500/0.50=0.20⋅1000≈6.3 m/s\tfrac{1}{2}k x^2 = \tfrac{1}{2}m v^2 \Rightarrow v = x\sqrt{k/m} = 0.20\sqrt{500/0.50} = 0.20 \cdot \sqrt{1000} \approx 6.3~\text{m/s}.

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