Chapter 4.1, Problem 46E

Physics Experiment Consider a physics laboratory experiment designed to determine an unknown mass. A flexible metal meter stick is clamped to a table with 50 centimeters overhanging the edge (see figure). Known masses $M$ranging from $$200$$grams to $$2000$$grams are attached to the end of the meter stick. For each mass, the meter stick is displaced vertically and then allowed to oscillate. The average time $t$(in seconds) of one oscillation for each mass is recorded in the table.

A model for the data that can be used to predict the time of one oscillation is

$$t=\frac{38M+16,965}{10(M+5000)}.$$

(a) Use this model to create a table showing the predicted time for each of the masses shown in the table above.

(b) Compare the predicted times with the experimental times. What can you conclude?

(c) Use the model to approximate the mass of an object for which $t=1.056$seconds.