A 6.0-kg box moving at 3.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Use the work-energy

Question

A 6.0-kg box moving at 3.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Use the work-energy theorem to find the maximum compression of the spring

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Thiên Di 4 years 2021-08-16T10:12:11+00:00 1 Answers 23 views 0

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  1. mocmien2
    0
    2021-08-16T10:13:37+00:00
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    Answer:

    8.5 cm

    Explanation:

    According to the work energy theorem, the total work done equals the change in the kinetic energy of the particle.

    Therefore,

    W = K_{total} \\

    where,

    K_{tot} = K_{f} - K_{i} \\

    Here, W is the total work done by force on the spring.

    plug in the following values:

    \\ K_{i} = \frac{mv^{2} }{2} \\ K_{f} = 0\\W = -\frac{kx^{2} }{2}

    We get:

    -\frac{kx^{2} }{2} = 0 -\frac{mv^{2} }{2}

    Solving this

    x = v\sqrt{\frac{m}{k} }

    Plug in the values given in the question:

    x = 3\sqrt{\frac{6}{7500} }

    x = 8.5 cm

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