Elastic Force and Energy – Short Lab Report – PHY 141/161
Name/Signature: __________________________
Name/Signature: __________________________
Name/Signature: __________________________
Introduction: Measure the elastic force F and elastic energy U of a spring as a
function of the amount of stretching or compression x. We expect that F(x) = kx,
with x measured relative to any fixed point. We expect that U(x) = ½kx2, with x
measured from the equilibrium length of the spring. Find the spring constant k in
both cases and compare. Answer the following questions:
1.
2.
3.
4.
5.
Is the spring elastic force F accurately given by our formula?
What is the value of k given by the force measurements?
Is the spring elastic energy U accurately given by our formula?
What is the value of k given by the energy measurements?
Do these two separate measurements agree on the value of k?
Data:
1. Force measurements, Table 1, Graph 1 (F vs. x). The slope value of k is given
by a straight line fit to the data.
2. Energy measurements, Table 2, Graph 2 (U vs. x). The quadratic value of k is
given by a quadratic fit to the data.
Analysis and Conclusions:
Force measurements
1. From the data, show the average value and standard deviation of the
values of k calculated from each data point:
(k ± k)(F) = ________ ± ________ N/m.
2. Show the value of k given by the slope of the graph:
kslope = ________ N/m.
3. Are these two values consistent? I.e., is (k ± k)(F) ≈ kslope ? YES or NO.
Energy measurements
1. From the data, show the average value and standard deviation of the
values of k calculated from each data point:
(k ± k)(E) = ________ ± ________ N/m.
2. Show the value of k given by the quadratic term of the graph:
kquad = ________ N/m.
3. Are these two values consistent? I.e., is (k ± k)(E) ≈ kquad ? YES or NO.
Comparison
1. Are the values obtained for k from the force data and from the energy data
consistent? I.e., is (k ± k)(F) ≈ (k ± k)(E)? YES or NO.
2. What is your best estimate for the value of k?
k ± k = ________ ± ________ N/m.