Assuming the Eq.(3) in the text is valid, what period of rotation of a mass of 0
ID: 2277726 • Letter: A
Question
Assuming the Eq.(3) in the text is valid, what period of rotation of a mass of 0.435 kg is to be expected for rotation radius of 0.200 m, if the outward pull which counters the spring inward pull for vertical mass-hanging string position at 0.200 m is delivered by a mass of 1.400 kg (pan included)? Use 9.810 m/s^2 for the acceleration of gravity.
Eqn 3: F= 4pi^2(mr)/T^2
2. If the quantities measured in order to verify Eq.(3) were obtained with values as in Problem 1, 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.
Explanation / Answer
a) Mg = 4pi^2(mr)/T^2
==> T = 2*pi*sqrt( mr/Mg) = 0.5 s
b)on left side %error = 0.01%
on right side = 0.01+0.001+0.05 = 0.061%