MasteringPhysics: Hwy 11 Elasticity and periodic motion Google Chrome https:// m

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MasteringPhysics: Hwy 11 Elasticity and periodic motion Google Chrome https:// mastering physics.com /myct/itemView assignment ProblemID 58678809 Session ASU PHY 111 Spring 2016 10577 HW Ela and periodic motion Problem 11.40 Weighing astronauts. Problem 11.40 Weighing astronauts. Part A In order to study the long-term effects of weightlessness, Find the force constant of the spring. 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 Submit My Answers Give Up Part B Find the mass of the astronaut. Submit My Answers Give Up N/m kg Close Resources previous l 8 of 10 l next Continue Provide Feedback

Explanation / Answer

time period od Simple Harmonic motion is given by T = 2 (m/k)1/2

T1 =  2 (m1/k)1/2

T2 =  2 (m2/k)1/2

T1 /T2 = ( m1 /m2 )1/2

1.3 /2.23 = ( 35.6 / m2 ) 1/2

35.6 /m2 = 0.339841943

m2 = 104.7545799 kg

This is the mass of astronaut and chair together.

So, mass of astronaut = 104.7545799 - 35.6 = 69.15457988 kg

from the first equation for chair alone -

1.3 = 2 (35.6 / k )1/2

0.206901426 = (35.6 / k )1/2

35.6/k = 0.0428082

k = 831.6163708 N/m

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