Two point particles are fixed on an x axis separated by...

Two point particles are fixed on an x-axis, separated by distance d. Particle A (located at the origin of the x-axis) has mass mA, and particle B has mass 3.00mA. A third particle C, with a mass of 75.0mA, is to be placed on the x-axis near particles A and B. In terms of distance d, at what x-coordinate should C be placed so that the net gravitational force on particle A from particles B and C is zero? (Hint: You should draw this. Particle A is at x = 0, and Particle B is at x = d. Further hint: Particle C is being pulled by A and B, so C will be in between the two other particles)

Transcript

00:01 So we're told we have two point -like particles on an axis here, the x -axis.

00:07 We have point a and point b.

00:09 They're separated by a distance d, which i've given the subscript ab here, to indicate how far apart those are.

00:18 And then we're asked how far away we should put a particle c so that the net force due to gravitation on a is zero.

00:28 And then we're told a little bit about the masses of the three objects here.

00:33 So we know that there is just some mass ma.

00:37 We know that the mass of b is three times the mass of ma, and we know that the mass of c is 75 times ma.

00:47 So to solve this, we have the sum of our forces in the x direction.

00:55 We want that to be equal to zero.

00:57 So that the net force on a is equal to zero.

01:02 So acting in the positive direction, we have the force from b, which is going to pull on a in the positive direction.

01:16 And we have a force acting in the negative direction, which is going to be c here.

01:22 And that's going to pull on a in the negative directions.

01:25 We want that to be equal to zero.

01:28 All right.

01:29 Tells us we can say the force from b has to be equal to the force from c.

01:36 And we know the form of the force due to gravity is newton's gravitational constant times m1 times m2 divided by r12 squared.

01:52 All right.

01:52 So this is the mass of any object one, the mass of any object two, and the distance between those squared...

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