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=2800 N/m), pulls himself back from the spring's equil length by 4 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

Given that spring constant is k = 2500 N /m a ) Time period T = 2 m/ k mass of the astrount is m = T^2 k / 4^2                                            = 1.00s * 2500N/m / 4^2                                             = 63.3 kg b) Potential energy stored in the spring when it is furthurest from its equilibrium length                   P. E = 1/2 k A^2                           = 1/2 * 2500N/m ( 3.00m)^2                           = 1.125*10^4 J c ) speed of the astrount v = A                                             = A k / m                                             = 3.00m * 2500 N/m / 63.3 kg                                            = 18.8 m/s d ) time taken by the oscillation is 1.00s because time period is independent of displacement

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