Elastic Potential Energy Physics Example 2

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Example 2

medium
A toy dart gun has a spring (k=250 N/mk = 250 \text{ N/m}) compressed by 0.08 m0.08 \text{ m}. If the dart has a mass of 0.01 kg0.01 \text{ kg}, what speed does the dart have when it leaves the gun?

Solution

  1. 1
    Elastic PE stored: PE=12kx2=12(250)(0.0064)=0.8 JPE = \frac{1}{2}kx^2 = \frac{1}{2}(250)(0.0064) = 0.8 \text{ J}.
  2. 2
    All PE converts to KE of the dart: 12mv2=0.8\frac{1}{2}mv^2 = 0.8.
  3. 3
    v=2×0.80.01=160≈12.65 m/sv = \sqrt{\frac{2 \times 0.8}{0.01}} = \sqrt{160} \approx 12.65 \text{ m/s}

Answer

v≈12.65 m/sv \approx 12.65 \text{ m/s}
The elastic PE stored in the compressed spring is fully converted to kinetic energy of the dart (assuming no friction). This energy conversion is the operating principle of spring-loaded devices.

About Elastic Potential Energy

Energy stored in an elastic object that has been stretched or compressed from its natural length.

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