Hooke’s law describes a certain light spring of unstretched length 34.8 cm. When one end is attached to the top of a doorframe and a 8.22 kg

Question

Hooke’s law describes a certain light spring of unstretched length 34.8 cm. When one end is attached to the top of a doorframe and a 8.22 kg object is hung from the other end, the length of the spring is 40.8 cm. (a) Find its spring constant. 1342.6 kN/m (b) The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 205 N. Find the length of the spring in this situation. m

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Thành Đạt 4 years 2021-08-06T01:08:50+00:00 1 Answers 12 views 0

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  1. minhkhoi
    0
    2021-08-06T01:09:58+00:00
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    Answer:

    a) k = 1343.6\,\frac{N}{m}, b) l = 0.501\,m\,(50.1\,cm)

    Explanation:

    a) The Hooke’s law states that spring force is directly proportional to change in length. That is to say:

    F \propto \Delta l

    In this case, the force is equal to the weight of the object:

    F = m\cdot g

    F = (8.22\,kg)\cdot (9.807\,\frac{m}{s^{2}} )

    F = 80.614\,N

    The spring constant is:

    k = \frac{F}{\Delta l}

    k = \frac{80.614\,N}{0.408\,m-0.348\,m}

    k = 1343.6\,\frac{N}{m}

    b) The length of the spring is:

    F = k\cdot (l-l_{o})

    l = l_{o} + \frac{F}{k}

    l=0.348\,m+\frac{205\,N}{1343.6\,\frac{N}{m} }

    l = 0.501\,m\,(50.1\,cm)

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