3. Astronaut in Space Since the acceleration due to earth\'s gravity is differen

Question

3. Astronaut in Space Since the acceleration due to earth's gravity is different in space, astronauts can't use bathroom scales to weigh themselves to determine their mass. Instead they sit in special chairs that oscillate and their mass is determined from q the oscillation frequency = k/m where k is the spring constant and m is the mass. The scale shown consists of a chair sitting on 8 identical springs in parallel. (a) An astronaut sits on the chair on earth and it oscillates with wo. If the astronaut looses mass in the trip to space, will the oscillation frequency increase, decrease, or stay the same? Explain. (b) An astronaut sits on the chair on earth and it oscillates with coo. The astronaut has the same mass in space but notices two of the springs have broken and are gone. Will the oscillation frequency increase, decrease, or stay the same (it may help to think of an effective spring constant by replacing all the springs with a single one of equivalent k)? Explain. (c) If the astronauts mass increases by 10% by how much will the oscillation frequencychange?

Explanation / Answer

(a)

Since mass inversely proportional to frequency, the frequency must decreases with lose of mass.

Thus, frequency decreases.

(b)

The spring constant decreses when springs were broken, because the springs are in parallel.

Thus, frequency decreases because spring constant proportional to frequency.

(c)

The change in frequency is

w_1*m_1=w_2*m_2

w_2/w_1=m_1/m_2

w_2/w_1=m_1/(m_1*1.1)

w_2/w_1=0.909

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