You hang different masses M from the lower end of a vertical spring and measure the period T for each value of M. You use Excel to plot T2 (

Question

You hang different masses M from the lower end of a vertical spring and measure the period T for each value of M. You use Excel to plot T2 (in s2) on the y-axis versus M (in kg) on the x-axis. The equation for the straight line that gives the best fit to your data is
y = 0.0569x + 0.00100.
A) What is the force constant k of the spring?
B) What is the mass of the spring?

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Dulcie 5 months 2021-08-25T18:19:25+00:00 1 Answers 0 views 0

Answers ( )

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    2021-08-25T18:21:22+00:00

    Answer:

    a)693.821N/m

    b)17.5g

    Explanation:

    We the Period T we can find the constant k,

    That is

    T = 2 \pi \sqrt{\frac{m}{k}}

    squaring on both sides,

    T^2=\frac{4\pi^2}{k}M +\frac{4\pi^2}{k}m_{spring}

    where,

    M=hanging mass, m = spring mass,

    k =spring constant

    T =time period

    a) So for the equation we can compare, that is,

    y=T^2=0.0569x+0.0010

    the hanging mass M is x here, so comparing the equation we know that

    \frac{4\pi^2}{k}=0.0569\\k= \frac{4\pi^2}{0.0569}\\k=693.821N/m

    b) In order to find the mass of the spring we make similar process, so comparing,

    \frac{4\pi^2}{k}m =0.001\\m=\frac{0.004k}{4\pi^2} =\frac{0.001*693.821}{4\pi^2}\\m=0.0175kg\\m=17.5g

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