A 5.0 kg box moving at 2.0 m/s on a horizontal, frictionless surface runs into a light horizontal spring of force constant 85 N/cm. Use the

Question

A 5.0 kg box moving at 2.0 m/s on a horizontal, frictionless surface runs into a light horizontal spring of force constant 85 N/cm. Use the work-energy theorem to find the maximum compression of the spring.

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Doris 3 years 2021-07-16T03:55:32+00:00 1 Answers 18 views 0

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  1. Farah
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    2021-07-16T03:57:13+00:00
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    Answer:

    x = 4.85 cm

    Explanation:

    From work energy theorem when dealing with a spring in compression, we know that total work done is;

    W_t = ½kx²

    Where;

    k is Force constant

    x is max compression

    Now, we know that this is also equal to the kinetic energy.

    K.E = ½mv²

    Thus;

    ½kx² = ½mv²

    Making x the subject;

    x = √(mv²/k)

    We are given;

    m = 5 kg

    v = 2 m/s

    k = 85 N/cm = 8500 N/m

    Thus;

    x = √(mv²/k)

    x = √(5 × 2²/8500)

    x = 0.0485 m

    x = 4.85 cm

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