Law of universal gravitation on three objects

[xvortx]

Homework Statement

Three(3) 10kg spheres form a triangle with the first sphere being at the top, the second sphere being at the bottom right cornern and the third sphere being at the bottom left corner. All sides of the triangle are 1.0m. Calculate the net gravitational force on the 3rd sphere.

Homework Equations

F=G(m1*m2)/r2

To find the gravitational force between two objects you would obviously use the above formula. This one has got me stuck. This is my first post, by the way. I would appreciate any help because this one has got me stuck.

 

[turin]

You must add the force due to both of the other masses. Assume that they add linearly.

 

[thomate1]

The law of universal gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In this scenario, we have three objects, each with a mass of 10kg, forming a triangle with sides of 1.0m.

To calculate the net gravitational force on the third sphere, we need to consider the gravitational forces between all three spheres. Let's label the spheres as A, B, and C, with A being at the top, B at the bottom right corner, and C at the bottom left corner.

First, we need to find the distance between each sphere. Since all the sides of the triangle are 1.0m, the distance between A and B is 1.0m, and the distance between A and C is also 1.0m. The distance between B and C can be found using the Pythagorean theorem, which gives us a distance of √2 m.

Now, we can use the formula F = G(m1*m2)/r^2 to calculate the gravitational force between each pair of spheres.

The force between A and B is FAB = G(10kg*10kg)/1.0m^2 = 100G N

The force between A and C is FAC = G(10kg*10kg)/1.0m^2 = 100G N

The force between B and C is FBC = G(10kg*10kg)/(√2 m)^2 = 50G N

Since the force between B and C is acting in the opposite direction as the forces between A and B and A and C, we need to subtract it from the net force.

Therefore, the net gravitational force on the third sphere (C) is:

Fnet = FAC - FBC = (100G N - 50G N) = 50G N

So, the net gravitational force on the third sphere is 50G N. I hope this helps clear your confusion. Keep up the good work!