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 = 50.4 g and M = 1.83 kg.)

(a) Find the acceleration of each mass.

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

(c) Through what angle does the rod rotate during this interval?

Explanation / Answer

Given that

Take m = 50.4 g and M = 1.83 kg.

The aaceleration of the small mass =GM/r2 =(6.67*10-11)(1.83)/(0.05)2 =4.88*10-8m/s2

The acceleration of the bigger mass m=Gm/r2 =(6.67*10-11)(0.0504)/(0.05)2 =1.34*10-9m/s2

b)

The time taken by the small mass is

dr/dt =GM/r2

t=(1/GM)integralr2dr limits from 0 to 1mm

t =(1/6.674*10^-11 * 1.83)*(10-9/3) =2.729s

The time taken for the bigger mass is

dr/dt =GM/r2

t=(1/GM)integralr2dr limits from 0 to 1mm

t =(1/6.674*10^-11 * 0.0504)*(10-9/3) =99.09s

c)

The angle is given by =1mm/60mm =0.01666radians =0.955degrees

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