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Conservation of Energy

AP Physics 1· difficulty 3/5

m v

A 0.40 kg0.40~\text{kg} block slides at 5.0 m/s5.0~\text{m/s} on a frictionless track toward a spring (k=100 N/mk = 100~\text{N/m}). Maximum compression?

  • A

    0.20 m0.20~\text{m}

  • B

    0.10 m0.10~\text{m}

  • C

    0.50 m0.50~\text{m}

  • D

    0.32 m0.32~\text{m}

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Explanation

12mv2=12kx2⇒x=vm/k=50.40/100=5(0.063)≈0.32 m\tfrac{1}{2} m v^2 = \tfrac{1}{2}k x^2 \Rightarrow x = v\sqrt{m/k} = 5\sqrt{0.40/100} = 5(0.063) \approx 0.32~\text{m}.

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