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 . Part A Find the force constant of the spring. (in N/m) Part B Find the mass of the astronaut. (kg)

Answer 1

Period of oscillation: T = 2*pi*sqrt(m/k)

Let the mass of the astronaut be M

So, time period of the spring when the astronaut is seated,

2.23 = 2*pi*sqrt((35.4+m) /k) -------- (1)

Also, when the chair alone oscillates,

1.25 = 2*pi*sqrt(35.4/k) ---------- (2)

So,  

Dividing eq(1) from. eq(2):

2.23/1.25 = sqrt((35.4+m) /35.4)

Solving, we get :

m = 77.3 ku <------- answer

Now, in eq(2)  

K = 894.4 N/m <------ answer