A Small Mass Measurement Instrument (SMMI) was used in Skylab to measure the mas

Question

A Small Mass Measurement Instrument (SMMI) was used in Skylab to measure the masses of biological samples, small animals, chemicals, and other such items used in life-sciences experiments while in orbit (see figure). The sample to be measured is strapped to a tray supported by leaf springs, and the mass is determined from the observed period of oscillation of the tray-and-mass. To calibrate this instrument, a test mass of 0.8 kg is first placed on the tray; the period of oscillation is then 1.193 s. Suppose that when the test is removed, and an unknown sample is placed on the tray, the period becomes 1.584 s. What is the mass of the sample? Assume that the mass of the tray (and the straps) is 0.4 kg. kg

Explanation / Answer

use the fact that

period = 2pi sqrt(m/k) so

1.193 = 2pi sqrt( 1.2 / k) and 1.584 = 2pi sqrt (m+0.4 / k)

if we take the ratio of these two equations

1.584 / 1.193 = sqrt ( m+0.4 / 1.2 )

square both sides

1.7629 = (m+0.4)/1.2

m = 2.515 kg is the mass of the sample

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