F = (4pi 2 mr) / T 2 Equation 3 Estimate the fractional error (%) on the left si
ID: 1278825 • Letter: F
Question
F = (4pi2mr) / T2 Equation 3
Estimate the fractional error (%) on the left side and on the right side of the equation based on the precision of the available equipment in class: the pulling mass is measured by slotted weights with precision of 10 gram, the rotating mass is measured by a beam balance with precision of 0.1 gram, the rotating radius is measured by a meter stick with 1mm divisions, and the period of rotation is determined by measuring the time for 20 revolutions, with 0.5 s uncertainty of that time due to the human reaction at operating a stop watch.
Please show detailed solution so I know how to do the problem.
Explanation / Answer
The given force equation is
F = 4 pi2 [mr / T2]
The force is balanced by weight
Mg = 4 pi2 [mr / T2]
T2 = 4 pi2 [mr / Mg]
T = 2 pi sqrt[mr / Mg]
= 2 pi * sqrt[0.435 * 0.2 / 1.400 * 9.8]
= 0.5 s
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The time period eqn is T = 2 pi sqrt[mr / Mg]
delta T / T * 100 = 1/2 [(delta m / m) + (delta r / r )+ (delta M/M)] * 100
= 1/2 [(10*10-3 / 0.435) + (10-3 / 0.2)+ (10-3/1.4)] * 100
= 1.44 %
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