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Conservation of Energy

AP Physics 1· difficulty 3/5

A 0.10 kg0.10~\text{kg} ball compresses a spring (k=200 N/mk = 200~\text{N/m}, compression 0.10 m0.10~\text{m}) at the bottom of a frictionless ramp. Released, the ball travels up the ramp. Using g≈10 m/s2g \approx 10~\text{m/s}^2, the maximum vertical height reached above the launch is

  • A

    1.0 m1.0~\text{m}

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  • B

    5.0 m5.0~\text{m}

  • C

    2.0 m2.0~\text{m}

  • D

    0.5 m0.5~\text{m}

Explanation

12kx2=mgh⇒h=(0.5⋅200⋅0.01)/(0.10⋅10)=1.0 m\tfrac{1}{2}k x^2 = m g h \Rightarrow h = (0.5 \cdot 200 \cdot 0.01) /(0.10 \cdot 10) = 1.0~\text{m}.

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