An astronaut measures her mass by means of a device consisting of a chair attached to a large spring.The period of oscillation she undergoes when set into motion is used to determine her mass.If her mass together with the chair is 172 kg,and the spring constant is 1250 N/m,what is the time 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 of the astronaut-chair system can be found using the formula:

T = 2π√(m/k)

where T is the period of oscillation, m is the total mass of the astronaut and the chair, and k is the spring constant.

Substituting the given values:

T = 2π√(172/1250)

T ≈ 3.42 s

Since the astronaut undergoes 10 full oscillations, the total time required is:

t = 10T

t = 10(3.42)

t ≈ 34.2 s

Therefore, the best choice is D, 23 s, which is closest to the calculated value of 34.2 s rounded to the nearest integer. None of the given choices is very close, so the closest one should be chosen, as mentioned in the instructions.

An Astronaut Measures Her Mass by Means of a Device