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 the vertical. Drawa
free-body diagram of one of the objects. (Do this on paper.Your
instructor may ask you to turn in this work.)

If two 130.0 kg objects are suspendedat the lower ends of cables 40.00
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 theseparation
distance in the expression for the gravitational force and assumethat
the deflection is extremely small compared to 1 m.)


m

possibility one:
r=1.000m-7.08nm
possibility two:
r=2.33x10^-4

Since i can only choose one answer, which one should i put down.Can i simplify 1.000-7.08x10^-9

Explanation / Answer

m = 130.0 kg, L = 40.00 m, d = 1.000 m 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)             = 3.5408 * 10-8 m

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