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 172 kg, and the time required for her to undergo 10 full oscillations is 27.0 seconds, what is the spring constant?
A) 400 N/m
B) 931 N/m
C) 148 N/m
D) 467 N/m

Question

Quizplus · Accepted Answer

To solve the problem, we can use the formula for the period of oscillation of a mass-spring system:

T = 2π√(m/k)

where T is the period of oscillation, m is the mass of the object, and k is the spring constant.

We are given the mass of the astronaut and chair (m = 172 kg) and the period of oscillation (T = 27.0/10 = 2.70 s). We can rearrange the formula above to solve for k:

k = (4π²m) / T²

Substituting the known values, we get:

k = (4π² x 172) / (2.70)² = 931 N/m

Therefore, the spring constant is 931 N/m. The answer is choice B.

An Astronaut Measures Her Mass by Means of a Device