How Far Does a Suspended Object Move Due to Gravitational Attraction?

[jawhnay]

Homework Statement

A student proposes to study the gravitational force by suspending 2 100 kg sperical objects at the lower ends of cables from the ceiling of a tall cathedral and measuring the deflection of the cables from the vertical. The 45 m long cables are attatched to the ceiling 1m apart. The first object is suspended and its position is carefully measured. The second object is suspended and the 2 objects atract each other gravitationally. By what disance has the first object moved horizontally from its initial position due to the gravitational attraction to the other object?

Homework Equations

The Attempt at a Solution

I found the force between the two objects using Newton's law of universal gravitation. Not sure where to go from there...

 

[Sourabh N]

Step 1) Draw a picture. What is the direction of the force on one object due to the other?

Step 2) Draw all the forces on each of the balls.

Do you see where to go from here?

 

[jawhnay]

Well, I drew a picture and the force on each of the balls is mg. so 100(9.8)=980 N and the force on one object due to other is 6.67 x 10^-7. I see a right triangle but not really sure how to approach it... My physics is kind of rusty so any hints would help..

 

[Sourabh N]

Okay, can you tell the direction (horizontal or vertical?) of the ball-Earth force and the direction of ball-ball force?

I am not sure about the numbers but the ball-Earth force's magnitude is much larger than ball-ball force's magnitude, just as you have shown.

 

[jawhnay]

The direction of of the ball-Earth force is vertical while the direction of the ball-ball force is horizontal?

 

[Sourabh N]

The direction of of the ball-Earth force is vertical while the direction of the ball-ball force is horizontal?

Right!

Now do the second step from my first post:
Step 2) Draw all the forces on each of the balls.

Since the ball isn't moving, all forces must balance.

 

[jawhnay]

I'm still really lost on how to find the distance that is has moved though =/

 

[Sourabh N]

We're getting there! Okay let me write all the steps.

1. Draw all forces on each balls. (There will be three: ball-ball in horizontal, ball-Earth in vertical and tension with components in vertical and horizontal.)
2. Balance forces, i.e. all forces in vertical direction should be zero, so should all forces in horizontal direction.

You should already have drawn pictures (at least two, one before the second ball comes in, one after).

Does that help?

 

[jawhnay]

not really... I'm still stuck in the same situation even with the forces drawn

 

[Sourabh N]

Okay let's go step by step. If there was no second ball, could you balance the forces? What's the magnitude and direction of each force on the first ball when there is no second ball?

 

[jawhnay]

100(9.8)=980 N which is the force on the ball going downward. The tension is 980 N going upward since the ball is not moving.

 

[Sourabh N]

Nice! Now, suppose another ball is drawn close to the first ball. First ball is attracted by the second ball, what will happen to it? Try to answer in a non-technical way.

 

[jawhnay]

the first ball will move towards the second ball in a horizontal motion.

 

[Sourabh N]

In this image, I have tried to show all the forces.
1. Can you label them?
2. Can you write all forces (or their components) in vertical direction?
3. Can you write all forces (or their components) in horizontal direction?

PS - a in that figure is the angle that you're looking for.

 

[jawhnay]

i've figured it out. I was under the impression that the 2 balls were hanging from separate cables 1 meter apart... yeah i got my diagram wrong. thanks a lot!

 

[Sourabh N]

i've figured it out. I was under the impression that the 2 balls were hanging from separate cables 1 meter apart... yeah i got my diagram wrong. thanks a lot!

They are indeed hanging from two separate cables o.o
In my figure, the dotted lines show the first ball system initially (without second ball), the solid lines on the other hand is the final configuration.

To clarify more, I have not drawn the second ball there at all.

Can you post your solution here so we know you figured it out correctly?