It is hard to measure the weight of an astronaut using a typical bathroom scale.

Question

It is hard to measure the weight of an astronaut using a typical bathroom scale. Instead, an astronaut can be strapped into a chair which is attached to springs and placed into oscillatory motion. Suppose the chair has a mass of 12.0 kg. The chair is attached to a spring with a spring constant of 870. n/m When set int oscillation, 14 oscillations take a total of 26.0 s. The amplitude of the oscillation is 12.0 cm.

a.) What is the period of oscillation of the astronaut?
b.) What is the mass of the astronaut?
c.) What is the maximum speed of the astronaut during the oscillation?
d.) Suppose the astronaut is set in motion a second time, but this time the amplitude of oscillation is 24.0 cm. Will the new frequency be greater, less than or equal to the frequency of the first trial?

Explanation / Answer

(a)

Period of oscillation,

T= 14/26 =0.53846 s

(b)w= 2pi/T = 2*3.14/0.53846=11.66 rad/s

hence,

w= root(k/m)

m = k/11.66^2

= 8700/11.66^2

=63.96 Kg

mass of man, mman=63.96-mass of chair= 63.96-12 = 51.96 Kg

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