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14 September, 09:29

A dart is loaded into a spring-loaded toy dart gun by pushing the spring in by a distance d. For the next loading, the spring is compressed a distance 8d. How much work is required to load the second dart compared to that required to load the first?

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  1. 14 September, 11:27
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    the work required for the loading of second dart is 64 times greater as work required for loading the first dart.

    Explanation:

    k = spring constant of the spring loaded toy dart gun

    x₁ = compression of spring to load the first dart = d

    x₂ = compression of spring to load the second dart = 8 d

    E₁ = Work required to load the first dart

    E₂ = Work required to load the second dart

    Work required to load the first dart is given as

    E₁ = (0.5) k x₁² = (0.5) k d²

    Work required to load the second dart is given as

    E₂ = (0.5) k x₂² = (0.5) k (8d) ² = (64) (0.5) k d²

    E₂ = 64 E₁

    So the work required for the loading of second dart is 64 times greater as work required for loading the first dart
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