An astronaut measures her mass by means of a device consisting of a chair attached to a large spring. Her mass can be determined from the period of the oscillations she undergoes when set into motion. If the spring constant is 1250 N/m and 27.0 seconds are required for her to undergo 10 full oscillations, what is the combined mass of the astronaut and chair?
A) 231 kg
B) 537 kg
C) 85.5 kg
D) 171 kg

Question

Quizplus · Accepted Answer

The period of oscillation is given by:$$T = 2\pi \sqrt{\frac{m}{k}}$$where m is the mass and k is the spring constant.Solving for m, we get:$$m = \frac{k T^2}{4\pi^2}$$Plugging in the given values, we get:$$m = \frac{(1250 N/m) (27.0 s)^2}{4\pi^2} = 231 kg$$

An Astronaut Measures Her Mass by Means of a Device