Question

in order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least 'massed'). one way in which this is done is to seat them in a chair of known mass attached to a spring of known force constant and measure the period of the oscillations of this system. the 42 kg chair alone oscillates with a period of 1.15 s, and the period with the astronaut sitting in the chair is 2.01 s. find the mass of the astronaut. round your answer to the first decimal place.

Answer 1

To find the mass of the astronaut, we can use the formula for the period of oscillation of a mass-spring system. Plugging in the given values and solving the equation, we find that the mass of the astronaut is 5.686 kg.

Step-by-step explanation:

To find the mass of the astronaut, we can use the formula for the period of oscillation of a mass-spring system:

T = 2π√(m/k)

Where T is the period of oscillation, m is the mass, and k is the force constant of the spring. We can rearrange the formula to solve for the mass:

m = (T^2)(k)/(4π^2)

Plugging in the given values:

m = (2.01^2)(k)/(4π^2)

m = (4.0401)(k)/(39.48)

m = (k)/(9.78)

Now, we know that the mass of the chair alone is 42 kg and it oscillates with a period of 1.15 s. Plugging in these values:

42 kg = (1.15^2)(k)/(4π^2)

Simplifying:

k = (42 kg)(4π^2)/(1.3225)

Finally, substituting the value of k back into the equation for mass:

m = (42 kg)(1.3225)/(9.78)

Calculating the mass:

m = 5.686 kg