Newton's Law & Gravitational F: Finding the Accl'n for a sphere

[BootyBabe]

Homework Statement

Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 1.20m. Two of the spheres have a mass of 2.8 kg, each.

The third sphere has an unknown mass, and is released from rest.

Considering only the gravitational forces that the spheres exert on each other, find magnitude of the initial acceleration of the third sphere.

Homework Equations

The Attempt at a Solution

I'm not sure how to attempt this question, where do I start> thanks!

 

[Doc Al]

Start with Newton's law of universal gravity.

 

[Moetasim]

As a scientist, it is important to approach problems like this using Newton's laws of motion and the law of universal gravitation. In this case, we can use Newton's second law, F=ma, to find the acceleration of the third sphere.

First, we need to calculate the gravitational force between each pair of spheres using the law of universal gravitation, F=G(m1m2)/r^2, where G is the gravitational constant (6.67x10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two spheres, and r is the distance between them.

In this case, we have three pairs of spheres, so we will calculate the gravitational forces between the first and second sphere, the first and third sphere, and the second and third sphere. We can then use vector addition to find the net force on the third sphere.

Once we have the net force, we can plug it into Newton's second law, F=ma, and solve for the acceleration of the third sphere. This will give us the magnitude of the initial acceleration of the third sphere.

It is important to note that this calculation only takes into account the gravitational forces between the spheres and assumes that there are no other external forces acting on the system. If there are other forces present, such as friction or air resistance, the acceleration of the third sphere may be different.

In conclusion, by using Newton's laws of motion and the law of universal gravitation, we can calculate the initial acceleration of the third sphere in this system. This approach can be applied to other similar problems involving gravitational forces between objects.