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 wan of the space capsule. A fellow astronaut then pulls her away from the wait and releases her. The spring's length as a function of time is shown in the figure What it her speed when the spring's length is 0 90 in? Express your answer to two significant figures and include the appropriate units

Explanation / Answer

part A) m = 71 kg

B)

given
Amplitude of motion, A = 0.4 m

Time period, T = 3 s

so, angular frequency, w = 2*pi/T

= 2*pi/3

= 2.094 rad/s

now Apply coservation of energy

0.5*k*A^2 = 0.5*k*x^2 + 0.5*m*v^2

==> 0.5*m*v^2 = 0.5*k*(A^2 -x^2)

v^2 = (k/m)*(A^2 - x^2)

v = sqrt((k/m)*(A^2 - x^2))

= w*sqrt(A^2 - x^2) (since sqrt(k/m) = w)

= 2.094*sqrt(0.4^2 - 0.1^2)

= 0.811 m/s

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