Question

An astronaut living on the space station is in a constant state of free-fall- the only force exerted on her and on the space station is the gravitational force due to earth. One method of determining her mass on the space station involves vibrational motion. An astronaut sits on the chair that vibrates horizontally at the end of a spring. A motion detector determines the amplitude of vibration and the speed of the chair as it passes through the equilibrium position. The spring has a spring constant of 1200 N/m, the amplitude of vibration is 0.50 m and the speed of the chair as it passes through equilibrium is 2.0 m/s. Using these data, find the combined mass of the chair and the astronaut.

Answer 1

Answer:

m = 75 kg

Explanation:

The maximum spring potential energy will equal the maximum kinetic enrgy

½mv² = ½kx²

m = kx²/v²

m = 1200(0.50²) / 2.0²

m = 75 kg