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Conservation of Energy

AP Physics 1· difficulty 3/5

A 0.50 kg0.50~\text{kg} block slides 3 m3~\text{m} down a frictionless 30∘30^\circ incline before contacting a spring at the bottom that compresses by 0.10 m0.10~\text{m} to stop it. Using g≈10 m/s2g \approx 10~\text{m/s}^2, the spring constant is closest to

  • A

    1500 N/m1500~\text{N/m}

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  • B

    3000 N/m3000~\text{N/m}

  • C

    750 N/m750~\text{N/m}

  • D

    300 N/m300~\text{N/m}

Explanation

Drop height before contact: h≈3sin⁡30∘=1.5 mh \approx 3 \sin 30^\circ = 1.5~\text{m} (ignoring small extra during compression). mgh=12kx2⇒k=2(0.5)(10)(1.5)/0.01=1500 N/mm g h = \tfrac{1}{2}k x^2 \Rightarrow k = 2(0.5)(10)(1.5)/0.01 = 1500~\text{N/m}.

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