A) A mass of 30.0 grams hangs at rest from the lower end of a long vertical spri

Question

A) A mass of 30.0 grams hangs at rest from the lower end of a long vertical spring. You add different amounts of additional mass ?M to the end of the spring and measure the increase in length ?l of the spring due to the additional mass. You plot your data in the form ?l (vertical axis) versus ?M (horizontal axis). Plotted this way, your data lies very close to a straight line that has a slope of .0126 m/kg. What is the force constant k of the spring? Use g=9.8 m/s^2

B)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=.0427x+.003

Units are not specified but are determined by the units of what is being graphed.

What is the force constant k of the spring? What is the mass of the spring?

Explanation / Answer

we have force= mg

or Kx= mg

now K(x+deltax)=(m+deltam)*g

so kx+ k*deltax= mg+ delta m *g

so slope is g/K

thus g/K=0.0126

or K= 9.8/0.0126

=777.78 N/m

B).T^2= 4*pi^2*M/K

so slope is 4*pi^2/K

thus 0.0427= 4*pi^2/K

so K= 923.61 N/m

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