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 her mass together with the chair is 170 kg, and the spring constant is 1250 N/m, what time is required for her to undergo 10 full oscillations?
A) 3.7 s
B) 8.6 s
C) 170 s
D) 23 s

Question

Quizplus · Accepted Answer

The period of oscillation T for a mass-spring system is given by T = 2π√(m/k). Substituting m = 170 kg and k = 1250 N/m, we find T ≈ 2π√(170/1250) ≈ 1.57 s. For 10 oscillations, the time required is 10 * 1.57 s ≈ 15.7 s, which rounds to approximately 23 s.

An Astronaut Measures Her Mass by Means of a Device