A Cavendish apparatus is shown in in the figure below. You can estimate the angl

Question

A Cavendish apparatus is shown in in the figure below. You can estimate the angle of rotation of the rod in the following way. Assume that the rod is massless, that there is no resistance to rotation, and that the same force acts on both masses. Then the acceleration of each mass may be computed independently, using Newton's second law. Furthermore, if the distance each mass moves is small compared with the separation between m and M, then the acceleration can be treated as constant. (Take m = 54.1 g and M = 2.18 kg.)

(a) Find the acceleration of each mass.

          m = 54.1 g ???

          M = 2.18 kg ???

(b) How long a time is required for each mass to move a distance of 1 mm?

          m = 54.1 g ???

          M = 2.18 kg ???

Explanation / Answer

Given: distance (r) between M (2.18 Kg) and m (0.0541 Kg) = 0.05 m

Therefore force F = GmM/r^2 = 6.67*10^-11*2.18*0.0541/0.05^2 = 3.146*10^-9 N

(a) acceleration of m (am)= F/m = 5.815*10^-8 m/s^2 acceleration of M (aM)= F/M = 1.443*10^-9 m/s^2

(b) We have second equation of motion as x = u*t + 1/2*a*t^2 where u is the initial speed (zero here) and t is the time

so t = (2*x/a)^0.5

Now for x = 1 mm = 10^-3 m

So time taken for M = (2*x/aM)^0.5 = (2*10^-3/1.443*10^-9)^0.5 = 1177.3 s = 0.327 hr

Time taken for m = (2*x/am)^0.5 = (2*10^-3/5.815*10^-8)^0.5 = 185.4 s = 3.1 minute

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