In the Cavendish balance apparatus shown in the figure 12.4 of the textbook (You

Question

In the Cavendish balance apparatus shown in the figure 12.4 of the textbook (Young and Freedman 12Th), suppose that m1 = 1.18 kg, m2 = 27.5 kg, and the rod connecting the pairs is 30.9 cm long.

(a) If, in each pair, m1 and m2 are 12.9 cm apart, find the net force.
(b) If, in each pair, m1 and m2 are 12.9 cm apart, find the net torque (about the rotation axis) on the rotating part of the apparatus.
(c) Does it seem that the torque in part (b) would be enough to easily rotate the rod?
Yes or No?

Thanks

Explanation / Answer

Solution: (a) For each pair of spheres: Fg = G m1 m2 / r^2       = 6.67 x 10^-11 * 1.18 * 27.5 / (0.129)^2       = 1.3 x 10^-7 N As forces for each pair are opposite in direction, Fnet = 0 Ans: Fnet = 0 (b) Distance to the rotation axis, L = 0.309 / 2                                                       = 0.1545 m Net Torque, net = 2 Fg L                               = 2 * 1.3 x 10^-7 * 0.1545                               = 4.02 x 10^-8 N.m Ans: Net torque = 4.02 x 10^-8 N.m (c) Ans: NO The torque is very small and may not be enough to rotate the rod.

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