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20 February, 00:43

One type of BB gun uses a spring-driven plunger to blow the BB from its barrel. Calculate the spring constant of its plunger's spring if you must compress it 0.283 m to drive the 0.0500-kg plunger to a top speed of 26.3 m/s. Assume that the barrel of the BB gun is horizontal.

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  1. 20 February, 01:00
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    431.83 N/m

    Explanation:

    Applying the law of conservation of energy,

    From the question,

    The kinetic energy of the plunger = energy stored in the spring

    1/2mv² = 1/2ke² ... Equation 1

    Where m = mass of the plunger, v = velocity of the plunger, k = spring constant of the spring, e = compression.

    make k the subject of the equation

    k = mv²/e² ... Equation 2

    Given: m = 0.05 kg, v = 26.3 m/s, e = 0.283 m

    Substitute into equation 2

    k = 0.05 (26.3²) / 0.283²

    k = 34.5845/0.080089

    k = 431.83 N/m
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