Constants PartA In order to study the long-term effects of weightlessness, astro

Question

Constants PartA 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 36.2 kg chair alone oscillates with a period of 1.00 s , and the period with the astronaut sitting in the chair is 2.21 s Find the force constant of the spring. k- N/m Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining PartB Find the mass of the astronaut. kg Submit Request Answer

Explanation / Answer

Given that the mass of the chair, m1 = 36.2 kg

Time periods, t1 (chair alone) = 1.00 s

Time period, t2 (with astronaut) = 2.21 s

To solve this problem, use the expression for the spring time periods -  

t1= 2* pi* SQRT (m1/k) -----------------------------------(i)
t2= 2* pi* SQRT (m2/k) ----------------------------------(ii)

Now, do (i) / (ii) -

t1/t2= SQRT (m1/m2)

=> m1/m2= (t1/t2)^2

Put the values -

36.2 / m2= (1.0 / 2.21)^2 = 0.205

=> m2 = 36.2 / 0.205 =  175.8 kg

Therefore, mass of astraunaut= m2 - m1= 175.8 - 36.2 = 139.6 kg (Answer of Part B)

Part A -

So we have from equation (i) -

1.00 = 2* 3.14 * SQRT (36.2 / k)

=> 1.00 / 6.28 = SQRT (36.2 / k)

=> 0.0253 = 36.2/k

=> k = 36.2 / 0.0253 = 1431 N/m

So, the force constant of the spring, k = 1431 N/m (Answer)

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