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)

Answer 1

Answer:

m = 77.3 kg

Explanation:

Time period of spring block system is given as

$T = 2\pi \sqrt{\frac{m}{k}}$

here we know

m = mass

k = spring constant

so now we have

$1.25 = 2\pi\sqrt{\frac{35.4}{k}}$

so we have

$k = 894.4 N/m$

Now time period of chair + astronaut is 2.23 s

so we have

$T = 2\pi \sqrt{\frac{m}{k}}$

$2.23 = 2\pi\sqrt{\frac{35.4 + m}{894.4}}$

$m = 77.3 kg$