Astronauts in space cannot weigh themselves by standing on a bathroom scale. Ins

Question

Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Supppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in the figure below.

(a) What is her mass if the spring constant is 230 N/m?
kg

(b) What is her speed when the spring's length is 1.08 m?
m/s

Explanation / Answer

Here ,

a)

time period of the harmonics , T = 6 s

spring constant , k = 230 N/m

Now, as T =2pi sqrt(m/k)

6 = 2pi * sqrt(m/230)

solving for m

m = 209.8 kg

her mass is 209.8 kg

b) let her speed if u m/s

using conservation of energy

0.5 * 209.8 * u^2 + 0.5 * 230 * (1.08 - 1)^2 = 0.5 * 230 *(1.4 - 1)^2

solving for u

u = 0.41 m/s

her speed when spring has a lenght of 1.08 m is 0.41 m/s

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