Elastic Force and Energy Short Lab Report PHY 141/161

Elastic Force and Energy – Short Lab Report – PHY 141/161

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. Is the spring elastic force F accurately given by our formula?

2. What is the value of k given by the force measurements?

3. Is the spring elastic energy U accurately given by our formula?

4. What is the value of k given by the energy measurements?

5. 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 ± Dk)(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 ± Dk)(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 ± Dk)(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 ± Dk)(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 ± Dk)(F) ≈ (k ± Dk)(E)? YES or NO.

2. What is your best estimate for the value of k?
k ± Dk = ______± ______N/m.