Ip three 650 kg masses are at the corners of an equilateral...

IP Three 6.50-kg masses are at the corners of an equilateral triangle and located in space far from any other masses. A) If the sides of the triangle are 1.91 m long, find the magnitude of the net force exerted on each of the three masses. B) How does your answer to part A change if the sides of the triangle are doubled in length?

Transcript

00:01 We are given that there is equilateral triangle and on the vertices of this triangle, there are three masses.

00:12 Mass of each of them is given to us.

00:15 This is 6 .5 kilograms.

00:20 This is the mass of each particle which is lying on the vertices here.

00:26 Now what we have to find is we have to find the force on each of them.

00:29 We know that whatever force will act on this, the same force will act on this and the same force will act on this because there is a symmetric.

00:39 So now let us calculate the force on one of them.

00:42 So the force which this charge, this mass will exert on this mass that can be calculated.

00:51 That would be attractive force.

00:53 I'm calling this force as a flat, let's say.

00:57 And now this particle will also attract this particle.

01:01 And the magnitude of the force will be f only both the forces are same because this mass and this distance is the same as this mass and this distance so the mass under consideration which is this mass will be experiencing definitely mass under consideration is this mass will be experiencing equal forces okay and this angle would be 60 degree that we know because an equilateral triangle.

01:38 So now to get the resultant of this resultant force, if i require the magnitude of resultant force, then that resultant force would be equal to square root off.

01:53 It would be equal to square root of.

01:57 F square plus f square plus two times of f cause 60.

02:11 So if we saw this, the net force will come out to be root 3 times of f.

02:20 And we know the value of f, right? it is the attractive force between two masses, which are separated by a distance l.

02:28 So this would be equal to root 3.

02:32 It is g and m1, m2 upon r square.

02:41 So we can put the value of all the variables here...