In order to study the long-term effects of weightlessness, astronauts in space m

Question

In order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least "massed"). One way in which this is done is to seat them in a chair of known mass attached to a spring of known force constant and measure the period of the oscillations of this system. The 35.4 kg chair alone oscillates with a period of 1.25 s, and the period with the astronaut sitting in the chair is 2.23 s.

a. Find the force constant of the spring. (units in N/m)

b. Find the mass of the astronaut. (units in kg)

Explanation / Answer

t=2(M/K)

K=42*35.4/(1.25)2=894.423kg/sec^2

2.23=2((35.4+m)/894.423)

35.4+m=112.666

mass of astronaut m=77.266kg

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