A Cavendish apparatus is shown in in the figure below. You can estimate the angl
ID: 1476176 • Letter: A
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 = 53.3 g and M = 2.05 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
(a)
acceleration of the small mass is
g = GM/d^2
= 6.674*10^-11 * 2.05 / 0.05^2
= 5.47*10^-8 m/s^2
Acceleration of the big mass g
g= Gm/d^2
= 6.674*10^-11 * 0.0533 / 0.05^2
= 1.42*10^-9 m/s^2
(b)
Time taken by the small mass
dr / dt = GM/r^2
t = (1/GM) integral r^2dr from 0 to 1mm
t = (1 / 6.674*10^-11 * 2.05 ) * (10^-9 / 3) = 2.436 sec
Time taken by the big mass
dr / dt = Gm/r^2
t = (1/GM) integral r^2dr from 0 to 1mm
t = (1 / 6.674*10^-11 * 0.0533 ) * (10^-9 / 3) = 93.7 s
(C)
angle = 1 mm / 60 mm = 0.01666 radians or 0.955 degrees
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.