A student measures the spring constant k of a spring by loading it and measuring the extension. (According to Hooke’s law, if l is the load and e is the extension, then k = l/e.) Assume five independent measurements are made, and the measured values of k (in N/m) are 36.4, 35.4, 38.6, 36.6, and 38.0.

a. Estimate the spring constant, and find the uncertainty in the estimate.

b. Find an approximate value for the uncertainty in the average of 10 measurements.

c. Approximately how many measurements must be made to reduce the uncertainty to 0.3 N/m?

d. A second spring, similar to the first, is measured once. The measured value for k is 39.3. Approximately how much is the uncertainty in this measurement?