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 180 N/m?
kg

(b) What is her speed when the spring's length is 0.70 m?
m/s

Explanation / Answer

Here ,

the equibrium length of the sprng = 1 m

a)

Here , the time period = 3 m

frequency , f = 1/3

Now,

1/3 = sqrt(k/m)/2pi

2pi/3 = sqrt(180/m)

solving for m

m = 41.1 Kg

her mass is 41.1 Kg

b)

Now for L = 0.70 m

Using conservation of energy ,

0.5 * 41.1 * v^2 + 0.5 * 180 * (1 - 0.7)^2 = 0.5 * 180 * 0.4^2

solving for v

v = 0.55 m/s

her speed when the spring's length is 0.55 m/s

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