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 time required for her to undergo 10 full oscillations is 27 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

The period of oscillation, T, of an object attached to a spring is given by:

T = 2π√(m/k)

where m is the mass of the object and k is the spring constant.

In this case, we know that the mass of the object plus the chair is 172 kg, and we need to find the spring constant. To do so, we need to rearrange the equation above to solve for k:

k = (4π^2 * m) / T^2

We are given that the time for 10 full oscillations is 27 seconds, so the period T is:

T = 27 s ÷ 10 = 2.7 s

Substituting the values for m and T into the equation for k, we get:

k = (4π^2 * 172 kg) / (2.7 s)^2
  = 931 N/m
Therefore, the answer is B, 931 N/m.

An Astronaut Measures Her Mass by Means of a Device