An astronaut sits on a chair that vibrates horizontally at the end of a string. A motion detector determines?

An astronaut sits on a chair that vibrates horizontally at the end of a string. A motion detector determines the amplitude of vibration and the speed of the chair as it passes through equilibrium position. The spring has a 1200N/m spring constant, the amplitude of vibration is 0.5m, and the speed of the chair as it passes through equilibrium is 2m/s. Using this data what is the combined mass of the chair and the astronaut.An astronaut sits on a chair that vibrates horizontally at the end of a string. A motion detector determines?The potential energy for a spring is given by the formula

U = (1/2)kx^2

where

U = potential energy

k = spring constant, here it is 1200 N/m

x = distance, here it is the amplitude 0.5 m



But with no other forces affecting the astronaut (at least I assume that is why an astronaut was chosen, so that he or she would be in orbit without having to worry about gravity or any other forces), then the maximum potential energy will be totally converted to kinetic energy when the spring is at it's equilibrium point. Which is

K = (1/2)mv^2

where

K = kinetic energy

m = mass of the astronaut and chair, what we want to know

v = velocity, in this case 2 m/s



Combining these gives

(1/2)kx^2 = U = K = (1/2)mv^2

Or just

(1/2)kx^2 = (1/2)mv^2

Solving for m

kx^2 = mv^2

m = kx^2/v^2

m = (9200 kg/s^2)(0.5 m)^2/(2 m/s)^2

m = 75 kg

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