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 240 N/m?
___ kg

(b) What is her speed when the spring's length is 0.78 m?
___ m/s

Explanation / Answer

Time period =3 sec

w=(2*pi)/(T)=2.094

w=sqrt(k/m)

So we got m=54.7 kg

(b)x=1+(0.4cos(wt)

Speed=dx/dt=0.4wsin(wt)

When x=0.78 ,t=1.028 sec

so

We got v=0.69 m/s

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