Gravitational Attraction-

In summary, in this conversation, the question is posed about the distance between two lead spheres suspended by cables. The discussion includes using the gravitational attraction between the spheres to find the angle and distance between them, as well as considering the negligible effect of the Earth's gravity. The final answer is found to be 6.8 * 10^(-10) degrees, a very small angle.
  • #1
bcjochim07
374
0
Gravitational Attraction-Please Help!

Homework Statement


Two 100kg lead sphers are suspended from 100m long massless cables. The tops of the cables have been anchored 1 m apart. What is the distance between the center of the spheres?

Homework Equations


Fg= Gm1m2/r^2


The Attempt at a Solution



Would I say find the force between them when they are just anchored, using 1m as my value for r? Then I thought I might use a force body diagram to find the angle that the cables are hanging and then the distance between the spheres. But the problem is, isn't the force going to increase as they get closer, so wouldn't they just keep moving toward each other?
 
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  • #2
Don't worry about it. Do what you said you were going to do. The movement toward each other is 'tiny', the correction to that is 'tiny'^2, or maybe even 'tiny'^3. Ignore it. It's completely insignificant.
 
  • #3
Ok, I summed up the forces on one sphere

Fx= GM^2/(1m)^2 In this case it is 6.67 *10^-7 N
Fy= T-mg T= 980 N

But how do I get an angle from that?
 
  • #4
Any thoughts on this question anybody??
 
  • #5
Fy is just mg. Now call theta the angle the cable makes with the vertical. Split T into x and y components. The total force on the mass is Fx+Fy+T=0.
 
  • #6
The change in the distance because the cables will both point to the center of the earth, which is equal to:
[tex] \frac {d l}{R_{earth}} [/tex]
wich is 0.016 mm is much bigger than the change because of the mutual attraction of the lead balls.
 
  • #7
Ty=980 and then does tension on x equal the force of gravity. I guess I don't understand what you mean by Fx + Fy + T = 0
 
  • #8
bcjochim07 said:
Ty=980 and then does tension on x equal the force of gravity. I guess I don't understand what you mean by Fx + Fy + T = 0

I mean that the sum of all of the forces on a stationary object is 0. Ty does equal 980N. What does Tx equal? Ty also equals T*cos(theta) and Tx equals T*sin(theta). Which you would know if you'd split T into x and y components. Does that suggest a way to find theta?
 
  • #9
I can't think of anything other than gravity between the spheresthat Tx would equal. When I draw my force body diagram, I have gravity from the other sphere along x and mg along y. But that doesn't seem to make the forces sum to zero. Once I figure Tx out though, I can draw a triangle and use trigonometry to find that angle.
 
  • #10
Tx does equal the gravitational attraction between the spheres! If you can use trig from there then you are good to go. They do sum to zero Ty=-Fy and Tx=-Fx.
 
  • #11
arctan(6.67E-10/980) = 6.8 * 10-10 degrees that's very tiny!
 
Last edited:
  • #12
bcjochim07 said:
arctan(6.67E-10/980) = 6.8 * 10-10 degrees that's very tiny!

You meant 6.67*10^(-7), right? And your final answer is correct but in radians, not degrees. But yes. Still very tiny. Gravitational force is extremely weak.
 

What is gravitational attraction?

Gravitational attraction is the force of attraction that exists between any two objects with mass. It is one of the four fundamental forces of nature and is responsible for keeping planets in orbit around the sun and for the formation of galaxies.

How does gravitational attraction work?

Gravitational attraction is caused by the curvature of space and time around massive objects. The more massive an object is, the more it curves the space around it, creating a gravitational pull that can be felt by other objects with mass.

What factors affect gravitational attraction?

The strength of gravitational attraction depends on two factors: the masses of the objects and the distance between them. The larger the masses of the objects and the closer they are to each other, the stronger the gravitational pull between them.

Can gravitational attraction be shielded or cancelled?

No, gravitational attraction cannot be shielded or cancelled. It is a fundamental force that exists between all objects with mass and cannot be turned off or blocked.

How is gravitational attraction related to Einstein's theory of relativity?

Gravitational attraction is a key concept in Einstein's theory of relativity. According to this theory, gravity is not a force but rather a curvature of spacetime caused by massive objects, and the strength of this curvature is what creates the effect of gravitational attraction.

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