An astronaut wants to find out his mass while in orbit, to find out if he is sta

Question

An astronaut wants to find out his mass while in orbit, to find out if he is staying healthy while in space. Since he can't use a bathroom scale (why not?), he attaches himself to a spring (k=3000 N/m), pulls himself back from the spring's equil length by 3 m, and times one oscillation to take 1 s. a.) What is the mass of the astronaut? kg b.) Find the potential energy stored in the spring when it is furthest from its equilibrium length. J c.) Find the speed of the astronaut when he passes through the spring's equilibrium. m/s d.) If he started at a displacement from equilibrium of 6 m instead, how long would one oscillation take now? s

Explanation / Answer

He can't use a bathroom scale because the bathroom scale measures the force of constraint between him and his environment...and when in orbit, there is no force of constraint because he drifts freely in the shuttle's cab.

Simply use the period formula for the mass and spring system:
T = 2*Pi*sqrt(m/k)

solve for m:
m = k*(T/(2*Pi))^2

And for the maximum SPE:
SPEmax = 1/2*k*xmax^2

And the KE at equilibrium:
KE = SPEmax, because of conservation of energy
KE = 1/2*m*vmax^2
1/2*m*vmax^2 = 1/2*k*xmax^2

solve for vmax:
vmax = xmax*sqrt(k/m)

Substitute expression for m:
vmax = 2*Pi*xmax/T

Summary:
A) m = k*(T/(2*Pi))^2
B) SPEmax = 1/2*k*xmax^2
C) vmax = 2*Pi*xmax/T

Data:
k:=3000 N/m; T:=1 sec; xmax:=3 m;

Results:
A) mass: m = 75.99 kg
B) SPEmax = 13500 Joules
C) vmax = 18.85 meters/second
D) Still 1 second...as long as the spring hasn't undergone failure. Period of a mass oscillating on a spring is independent of amplitude.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.