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

Question

A student proposes to measure the gravitational constant G by suspending two spherical objects from the ceiling of a tall cathedral and measuring the deflection of the cables from the vertical. Draw a free-body diagram of one of the objects.

If two 120.0 kg objects are suspended at the lower ends of cables 45.00 m long and the cables are attached to the ceiling 1.000 m apart, what is the deflection of each object?

(Use 1.000 m for the distance in the gravitational force and assume that the deflection is extremely small.)

Explanation / Answer

If the two objects are slighly deflected towards one another by an angle , the restoring force is equal to mg sin , which is the component of their weight directed horizontally. For a very small deflection, sin .

The weight of each object is (120 kg)(9.81 m/s2) = 1177 N

The force between them is Gm1m2/r2 = (6.6738 * 10-11 m3/kg s2)(120 kg)2/(1 m)2 = 9.61 * 10-7 N

So we know mg sin mg = (1177 N)() = 9.61 * 10-7 N

Solving for , = (9.61 * 10-7)/(1177) = 8.164 * 10-10 radians

The deflection is (45 m)(8.164 * 10-10 radians) = 3.674 * 10-8 m or about 37 nm

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