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 36.2kg chair alone oscillates with a period of 1.15s , and the period with the astronaut sitting in the chair is 2.20s

Part A: Find the force constant of the spring.

Part B: Find the mass of the astronaut.

Answer 1

Answer:

a. K = 1080.61 N/m

b. mₐ = 96.28 kg

Explanation:

T = 2π * √ m / K

T₁ = 2π * √m₁ / K , T₂ = 2π * √m₂ / K

m₁ = 36.2 kg , m₂ = m₁ + mₐ

T₁ = 1.15 s , T₂ = 2.2 s

Equal period to determine the force constant of the spring

a.

K = 4π²* m₁ / T₁²

K = 4π² * 36.2 kg / 1.15² s

K = 1080.61 N/m

So replacing and solve can find m₂

b.

m₂ = T₂² * m₁ / T₁²   ⇒  m₂ = 2.20² s * 36.2 kg  / 1.15 ² s

m₂ = 132.48

mₐ = m₂ - m₁

mₐ = ( 132.48 - 36.2 ) kg = 96.28 kg