What is the Maximum Gravitational Force Between Two Uniform Spheres?

[paprika]

The problem is as follows:

A bowling ball (mass = 7.2kg, radius = 0.11 m) and a billiard ball (mass = 0.39 kg, radius = 0.028 m) may be treated as uniform spheres. What is the magnitude of the maximum gravitational force that each can exert on the other.

I already asked my physics teacher for help, sat with the man for like 10 minutes after shool but he still couldn't help me under stand why the answer to the problem was what it was.

I am thinking, because of how the question is stated, that the answer is the maxiumum amount of force that both balls can sucessfully exert on each other. It cannot be the greater force exerted by one or the because in that case the other ball wound't be able to exert anywhere near that amount of force and the question says ".. maxiumum gravitational force that each can exert on the other..." - stressing the word EACH.

So coudl someone explain to me what kind of answer this problem is looking for? Thanks.

 

[Skomatth]

The gravitational force between 2 objects is equal. Newton law of universal gravitation says so. Now think of what situation the 2 balls could be in that would maximize the force.

 

[paprika]

?? :( Still lost sorry

 

[Skomatth]

Due to gravity, I am exerting a force on you right now. You are exerting the exact same force on me. Understand that?

 

[tyco05]

Newtons law of Universal gravitation:

$$F=\frac{Gm_1 m_2}{r^2}$$

So, the force exerted on one body by the other is dependent on the masses (which we can't change) and the distance between the two bodies.

What situation would make this force a maximum?






Obviously if they were really really really far away from each other, the force would be small.

How close can they get? What would the force be when they were that close?

 

[paprika]

Newtons law of Universal gravitation:

$$F=\frac{Gm_1 m_2}{r^2}$$

So, the force exerted on one body by the other is dependent on the masses (which we can't change) and the distance between the two bodies.

What situation would make this force a maximum?






Obviously if they were really really really far away from each other, the force would be small.

How close can they get? What would the force be when they were that close?

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[teclo]

the strength of the gravitational force is related to the inverse square of the distance between the center of mass of the two objects. try thinking about this problem in two dimensions. imagine you cut a slice out of the exact center of each sphere (with radius exactly the same as the sphere) and then put them as close as possible to each other. what's the distance between the center of each circle?

now you know the distance the force is acting over, which should make the problem relatively simple.

 

[Phymath]

the max is when they are right next to each other touching, the force of gravity acts on the center of mass of the object (ie a point mass in the center of each ball) at least that's my understanding, so u min the distance makes a max in the force that EACH exterts on each other, if ur having trouble understanding this, try understanding that if they were far away from each other an no other masses in the universe exsisted, they would attract each other, and ur problem i pressume is that yes the smaller (lower massed) ball would have a greater acceleration toward the bigger (more massive) ball, however they have the same FORCE acting on each ball and they are attracked to the center of mass of the system of the two balls, hope that helps...