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.

Part B) Find the mass of the astronaut.

Please include formulas so i main learn from where you got the answers

Explanation / Answer

m= mass of chair = 35.6 kg

T1 = alone time period = 1.30 s

T2 = with astronaut time period = 2.23 s

M = mass of astronaut = ?

force constant or spring factor = k = ?

from spring time period equation :

T = 2*pi ( interia factor / spring factor )1/2

= 2*pi ( m/ k)1/2

so T1 = 2*pi ( m/ k)1/2

1.30 = 2*3.14*( 35.6 / k)1/2   ---------------------1

T2 = 2*pi ( m+M / k)1/2

2.23 = 2*3.14 ( 35.6 + M / k)1/2   ----------------------2

divide eq 1 &2

1.30 / 2.23 = 2*3.14*( 35.6 / k)1/2 / 2*3.14 ( 35.6 + M / k)1/2

0.582 = (35.6 / 35.6 + M)1/2

( 0.582)2 = 35.6 / 35.6 + M

12.05 + 0.338 M = 35.6

M = 69.67 Kg

a) from eq 1:

1.30 = 2*3.14*( 35.6 / k)1/2   

0.0428 k = 35.6

k = 831.77 N/m

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.