1. Assuming the Eq.(3) in the text is valid, what period of rotation of a mass o
ID: 2136530 • Letter: 1
Question
1. 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.
Mg = 4pi^2(mr)/T^2 --> EQUATION 3
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.
I KNOW ANSWER 1, T=0.5 SECONDS. I NEED THE ANSWERS FOR #2 WITH THE WORK SHOWN TO RECIEVE FULL POINTS.
Explanation / Answer
take log on both side
log(Mg)= log(4*Pi*Pi*m*r/T^2 )
logM + log(g)=log(4*Pi*Pi)+log(m)+log(r)-2log(T)
differentiate
dM/M + dg/g = 0 + dm/m + dr/r -2dT/T
dx is the possible change in quantity x .it can be positive or negative because it is uncertainity so all the symbols will become positive for finding maximum error hence
dM/M + dg/g = dm/m + dr/r + 2dT/T
i don't know what is M and m as you have not cleared in your question.but you have all the values except dT which you need to find.
M,g,m,r,T will be taken from part1.
i hope you will get my point.
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