Respuesta :
The maximum speed of an astronaut is 12.5cm/s.
If, the astronaut uses body mass measurement device to measure her mass, then the speed can be calculated easily.
How to calculate speed of an astronaut in space?
By differentiating angular frequency, and displacement of mass with respect to time, then speed can be calculated.
Calculation:
We know,
Force constant of the spring, k = 3000 N/m
Mass of an astronaut, m = 69 kg
Amplitude of the oscillation, x max = 1.9cm = [1.9 cm]*[1 m/100 cm] = 0.019m
We need to find the vmax.
The angular frequency ω is given by,
ω = √[k/m]
The displacement of the mass m from the men position in case of simple harmonic motion is given by,
x = xmax*cos[ωt + φ]
Differentiating above relation with respect to time we get the velocity of the object at any time t during the motion.
v = -ω*xmax*sin[ωt + φ]
v = - vmax*sin[ωt + φ]
Here we have the velocity amplitude {maximum velocity} vmax given as
vmax = ω*xmax
vmax = √[k/m]*xmax
vmax = √[(3000 N/m)/(69kg )]*[0.019 m]
vmax = 0.125m/s
vmax = 12.5 cm/s
Hence the maximum speed of an astronaut is 12.5cm/s
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