Problem 11.40 Weighing astronauts. In order to study the long-term effects of we

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Problem 11.40 Weighing astronauts. 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 35.6kg  chair alone oscillates with a period of 1.30s , and the period with the astronaut sitting in the chair is 2.23s . Part A Find the force constant of the spring. k =
N/m SubmitMy AnswersGive Up Try Again Part B Find the mass of the astronaut. m =
kg Problem 11.40 Weighing astronauts. 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 35.6kg  chair alone oscillates with a period of 1.30s , and the period with the astronaut sitting in the chair is 2.23s . Problem 11.40 Weighing astronauts. 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 35.6kg  chair alone oscillates with a period of 1.30s , and the period with the astronaut sitting in the chair is 2.23s . 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 35.6kg  chair alone oscillates with a period of 1.30s , and the period with the astronaut sitting in the chair is 2.23s . 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 35.6kg  chair alone oscillates with a period of 1.30s , and the period with the astronaut sitting in the chair is 2.23s . Part A Find the force constant of the spring. k =
N/m SubmitMy AnswersGive Up Try Again Part A Find the force constant of the spring. k =
N/m SubmitMy AnswersGive Up Try Again k =
N/m k =
N/m SubmitMy AnswersGive Up Try Again Try Again Try Again Part B Find the mass of the astronaut. k =
N/m

Explanation / Answer

for only chair...

time period = 2*pi * sqrt ( m / k )

so.. 1.3 = 2*pi * sqrt ( 35.6 / k )

so.... k = 831.6164 N/m

now for astraunot ..

time period = 2*pi * sqrt ( m / k )

2.23 = 2*pi * sqrt ( (35.6 + m ) / 831.6164 )

so... mass of asronaut = 69.15458 kg

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