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Conservation of Energy

AP Physics 1· difficulty 3/5

A 0.40 kg0.40~\text{kg} block sliding at 3.0 m/s3.0~\text{m/s} on a frictionless surface compresses a spring with k=1500 N/mk = 1500~\text{N/m} until it stops. How far does the spring compress?

  • A

    0.049 m0.049~\text{m}

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  • B

    0.30 m0.30~\text{m}

  • C

    0.025 m0.025~\text{m}

  • D

    0.10 m0.10~\text{m}

Explanation

12mv2=12kx2⇒x=vm/k=3.00.40/1500≈0.049 m\tfrac{1}{2} m v^2 = \tfrac{1}{2}k x^2 \Rightarrow x = v\sqrt{m/k} = 3.0\sqrt{0.40/1500} \approx 0.049~\text{m}.

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