Newton's Law of Universal Gravitation deflection

[_mae]

Homework Statement

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. If two 155.0 kg objects are suspended at 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 the distance in the gravitational force and assume that the deflection is extremely small.)

Homework Equations

I think this equation should be used: Fg = (G)([m1*m2]/r^2)

G would be the universal gravitational constant: G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}

The Attempt at a Solution

I'm confused at what exactly the problem is looking for, though I know the answer is looking for a distance in meters. I don't know which variable to solve for in the equation.

I do know that m1 and m2 are each 155 kg, and when multiplied together equal 24,025 kg. In my textbook, it says that r is the distance separating the two masses. So if each cable is 40 m long, the total distance between them (which would be r) would equal 80 m. r^2 would then be 6400. From here, I don't know what to look for.

If my answer should be in meters, and I already know G, r^2, and both masses, then that leaves me with solving for Fg, which is in Newtons.

My homework is on WebAssign, and I've noticed that the numbers I put in bold (red in my actual homework) are the only numbers used to solve the problem, so I'm assuming I don't need 1.000 m to solve it.

Please help!

 

[Dick]

The problem told you that the masses were 1m apart. Why did you change it to 80m? You do need the 1m figure. Your equation will yield a very small force. The 40m length will come in when you compute the deflection. Hint: a small amplitude pendulum is a harmonic oscillator.

 

[_mae]

Well, that's what I initially thought -- the 2 masses were 1m apart attached to the cables on the ceiling. But then my textbook showed a somewhat similar example with a different diagram. It showed 1 cable hanging from a ceiling which was attached to a horizontal rod with objects of mass at both ends (it kinda looks like an upside-down T). So this is what I'm picturing now. That's why I started to think the distance between them was 80m.

I'm still confused though. How does the 40 m come in the problem when there's no other variable that would solve for a distance?

 

[Dick]

That sounds like a different experiment. Forget it. The 40m comes in because once you compute the force you need to compute the deflection coming from the force. And that means you need to figure out how much a pendulum of length 40m deflects subjected to an external force.

 

[_mae]

I'm sorry, but now I'm even more confused than before.

From what you're saying, I should use the equation I gave above to calculate Fg, the magnitude of the gravitational force between the two masses. But from there I don't know how to calculate the deflection of a 40m length. Am I missing another equation?

 

[Dick]

You need the relation between the applied force and the deflection of the hanging object (which a basically a pendulum). Assume the object is displaced from the vertical by some angle theta. The forces acting on the object will be the horizontal gravitational force, the vertical weight of the object and the tension force inclined at the angle theta. Can you relate theta to the applied force?