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16 October, 09:18

A vertical spring has a length of 0.25 m when a 0.175 kg mass hangs from it, and a length of 0.775 m when a 2.075 kg mass hangs from it. gA. What is the force constant of the spring, in newtons per meter?

B. What is the unloaded length of the spring, in centimeters?

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  1. 16 October, 12:07
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    A) 35.5N/m b) 20.1cm

    Explanation:

    Using Hooke's law;

    F = Ke where F is the weight of the object = mass of the object in kg * acceleration due to gravity in m/s^2 and k if the force constant of the spring in N/m and e is the extension of the spring which original length of the spring - new length after extension in meters

    For the first body, m*g = K * (0.25 - li)

    Where li is the initial length of the spring

    0.175*9.81 = k (0.25-li)

    1.72 = k (0.25-li) as equation 1

    For the second body, m * g = K * (0.775-li)

    2.075*9.81 = k (0.775-li) equation 2

    20.36 = k (0.775-li)

    Make li subject of the formula;

    li = 0.775 - 20.36/k

    Substitute for li in equation 1

    1.72 = k (0.25 - (0.775 - 20.36/k))

    1.72 = k (0.25 - 0.775 + 20.36/k)

    Open the bracket with k

    1.72 = 0.25k - 0.775k + 20.36 (since k cancel k)

    Collect the like terms:

    1.72 - 20.36 = - 0.525k

    - 18.64 = - 0.525k

    Divide both side by - 0.525

    -18.64/-0.525 = - 0.525/-0.525k

    K = 35.5N/m

    B) substitute for k in using

    li = 0.775 - 20.36/k

    li = 0.775 - 20.36/35.5

    li = 0.775 - 0.574

    li = 0.201 in meters

    li = 0.201 * 100 centimeters = 20.1cm
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