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Conservation of Energy

AP Physics 1· difficulty 3/5

A 0.20 kg0.20~\text{kg} ball is dropped from rest, 0.50 m0.50~\text{m} above a spring with k=100 N/mk = 100~\text{N/m}. Using g≈10 m/s2g \approx 10~\text{m/s}^2, the maximum spring compression is closest to (ignore spring's contribution to height during compression):

  • A

    0.14 m0.14~\text{m}

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  • B

    0.20 m0.20~\text{m}

  • C

    0.10 m0.10~\text{m}

  • D

    0.04 m0.04~\text{m}

Explanation

Drop energy: mgh=0.20⋅10⋅0.50=1.0 Jm g h = 0.20 \cdot 10 \cdot 0.50 = 1.0~\text{J} (over 0.50 m0.50~\text{m}). Set 12kx2=1.0⇒x=0.02≈0.14 m\tfrac{1}{2}k x^2 = 1.0 \Rightarrow x = \sqrt{0.02} \approx 0.14~\text{m}.

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