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. Suppose 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 (Figure 1) .

https://session.masteringphysics.com/problemAsset/1383590/6/knight_Figure_14_36.jpg

What is her mass if the spring constant is 250 N/m?

What is her speed when the springs length is 1.0m?

Explanation / Answer

according to figure equilibrium position is at x = 1.0m

at eqm kx = mg

250*1 = m*10

m = 25 kg

at eqm KE = U

1/2*M*V^2 = 1/2*K*x^2

1/2 *25*v^2 = 1/2*250*(0.4)^2

v^2 = 1.6

v = 1.26m/s

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