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 220 N/m? 50.15 kg Your answer is correct.

(b) What is her speed when the spring's length is 0.96 m?

I am stuck on part B of this problem. If anyone could explain how to do it in detail it would be appreciated! Thanks!!

Explanation / Answer

b) let her speed if u m/s

From the figure it is clear that the natural length of the spring is 1.0 m and the maximum

elongation (Amplitude) is 0.4 m.

When the length of

the spring is 1.06 m its elongation is 0.96-1.0 = 0.04 m, hence the

elastic potential energy in this position is given by

using conservation of energy

0.5 * 50.15 * u^2 + 0.5 * 220 * (0.96-1)^2 = 0.5 * 220 *(1.4 - 1)^2

solving for u

u = 0.794 m/s

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