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 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.

Explanation / Answer

use the spring time period eqn

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

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

36.2/m2= (1.15/2.2)^2
m2= 132.48 kg

mass of astraunaut= m2 - m1= 132.48 - 36.2 = 96.28 kg

Now
1.15 = 2* 3.14 * SQRT (36.2/k)
36.2/k = 0.183^2

Spring constant k= 1080.951 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.