In order to study the long-term effects of weightlessness, astronauts in space m

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 35.6 kg chair alone oscillates with a period of 1.30 s , and the period with the astronaut sitting in the chair is 2.23 s .

Part A

Find the force constant of the spring.

nothing

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Part B

Find the mass of the astronaut.

77.26677.266

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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 35.6 kg chair alone oscillates with a period of 1.30 s , and the period with the astronaut sitting in the chair is 2.23 s .

Part A

Find the force constant of the spring.

k =

nothing

  N/m  

SubmitRequest Answer

Part B

Find the mass of the astronaut.

m =

77.26677.266

  kg  

SubmitPrevious AnswersRequest Answer

Incorrect; Try Again; 5 attempts remaining

Explanation / Answer

a) from the relation

time T = 2pisqrt*m/k)

k = 4pi^2m/T^2

here m = 35.6 kg

T = 1.3 s

k = 4*3.14^2*35.6/1.3^2

k = 830.8 N/m

b) now T = 2.23 sec

T = 2pisqrt((m+M)/k)

m+M = k*(T/2pi)^2

m+M = 830.8*(2.23/2*3.14)^2 = 104.76

M = 104.76-35.6 = 69.16 kg

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