A student proposes to measure the gravitational constant G by suspending two sph

Question

A student proposes to measure the gravitational constant Gby suspending two spherical objects from the ceiling of a tallcathedral and measuring the deflection of the cables from thevertical. Draw a free-body diagram of one of the objects.

If two 145.0 kg objects are suspendedat the lower ends of cables 35.00 mlong and the cables are attached to the ceiling 1.000 m apart, whatis the deflection of each object? (Use 1.000 m for the distance inthe gravitational force and assume that the deflection is extremelysmall.)

Explanation / Answer

m = 145.0 kg, L = 35.00 m, d = 1.000 m G=6.667 *10-11m3 kg-1s-2 g=9.8 m/s2 when equilibrium, the cable will make angle withvertical. gravitaional force F = Gm2/d2 tan = F/(mg) deflection = Lsin ˜ L*tan = L*F/(mg) =L*Gm/(gd2) = 3.455 *10-8 m

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