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) .

What is her mass if the spring constant is 270N/m ?

What is her speed when the spring's length is 1.2m ?

Explanation / Answer

since the spring performs a simple harmonic motion whose eq. is

y = .4coswt       about the mean length of spring which is 1

   so y= .4coswt    where w = sqrt(k/m)

        also   Time period= 3 (from graph)

1/f = 3         f=1/3

    w=2pif = 2pi/3 so

   2pi/3 = sqrt(270/m)

m=61.615 kg

       at y =.2 = .4coswt

      wt= pi/3    t = pi/3w

    and v=dy/dt = -.4wsinwt

   at wt = pi/3       

   v = -.4*2pi/3 *[sqrt(3)]/2

        = -.725m/s   or   0.725 m/s

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