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2 May, 04:56

A 30.0 g arrow is shot by William Tell though an 8.00 cm thinck apple sitting on top of his son's head. If the arrow enters the apple at 30.0 m/s and emerges at 25.0 m/s in the same direction, with what force has the apple resisted the arrow?

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  1. 2 May, 04:59
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    The resisting force of the apple, causes an impulse into the arrow. The change of momentum of the arrow is then equal to the impulse.

    dp = F dt

    F = dp/dt

    The change of momentum is just

    dp = mv2 - mv1 = m (v2 - v1).

    The amount of time,

    dt = dist / v_ave

    dt = dist / ((v1 + v2) / 2)

    Therefore,

    F = m (v2 - v1) / dist * (v1 + v2) / 2

    F = 1/2 * m (v2^2 - v1^2) / dist

    F = 1/2 * 30e-3 * (30^2 - 25^2) / 8e-3

    F = 515.625 N
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