When a block of mass M, connected to the end of a spring of mass ms = 7.40 g and force constant k, is set into simple harmonic motion, the period of its motion is
T = 2π √M + (ms/3)/k
A two-part experiment is conducted with the use of blocks of various masses suspended vertically from the spring, as shown in Figure P15.68.
(a) Static extensions of 17.0, 29.3, 35.3, 41.3, 47.1, and 49.3 cm are measured for M values of 20.0, 40.0, 50.0, 60.0, 70.0, and 80.0 g, respectively, Construct a graph of Mg versus x, and perform a linear least-squares fit to the data. From the slope of your graph, determine a value for k for this spring.
(b) The system is now set into simple harmonic motion, and periods are measured with a stopwatch. With M = 80.0 g, the total time for 10 oscillations is measured to be 13.41 s. The experiment is repeated with M values of 70.0, 60.0, 50.0, 40.0, and 20.0 g, with corresponding times for 10 oscillations of 12.52, 11.67, 10.67, 9.62, and 7.03 s. Compute the experimental value for T from each of these measurements. Plot a graph of T 2 versus M, and determine a value for k from the slope of the linear least squares fit through the data points. Compare this value of k with that obtained in part (a).
(c) Obtain a value for ms from your graph and compare it with the given value of 7.40 g.

Transcribed Image Text:

Figure P15.68