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18 February, 14:47

In a spring gun, a spring of mass 0.240 kg and force constant 3100 N/m is compressed 2.00 cm from its unstretched length. When the trigger is pulled, the spring pushes horizontally on a 5.5*10-2 kg ball. The work done by friction is negligible. Calculate the ball's speed when the spring reaches its uncompressed length ignoring the mass of the spring.

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  1. 18 February, 15:17
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    The ball's speed when it reaches its uncompressed length = 0.73m/s

    Explanation:

    The speed of the ball is greatest when acceleration is zero and the net force on the ball is zero.

    Given:

    Force constant = 3100Nm

    Compressed length = 2.0cm = 0.02m

    Spring mass = 0.240kg

    Mass of barrel = 5.5 * 10^-2kg

    Resistant force, F = ma

    F = 5.5*10^-2 * 9.8 = 0.539N

    0.538/3100 = 1.738*10^-4m

    Initial force on the ball = (3100 * 0.02) - 0.539

    Initial force on ball = 62 - 0.539 = 61.46N

    Final net force on ball = 0N

    Mean net force of ball = 1/2 (61.46 + 0) = 30.73N

    Net on ball = 30.73 * (1.74*10^-4) = 5.35*10^-3J

    Transfer to KE = 1/2mv^2

    V^2 = (5.35*10^-3) / 0.01

    V^2=0.535

    V = Sqrt (0.535)

    Vmax = 0.73m/s
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