The drawing shows three particles far away from any other...

The drawing shows three particles far away from any other objects and located on a straight line. The masses of these particles are $m_{\mathrm{A}}=363 \mathrm{~kg}, m_{\mathrm{B}}=517 \mathrm{~kg}$, and $m_{\mathrm{C}}=154 \mathrm{~kg} .$ Find the magnitude and direction of the net gravitational force acting on (a) particle $\mathrm{A}$, (b) particle $\mathrm{B}$, and (c) particle $\mathrm{C}$.

Transcript

00:01 Hi there, so for this problem, we have the drawing of the shows three particles far away from any other objects.

00:10 And then we are given the following masses for this.

00:14 So the mass of a is equal to 363 kilograms.

00:21 The mass of b also given that is equal to 517 kilograms.

00:26 And the mass of c is 154 kilograms.

00:31 So we need to find the metadata and the eruption of the net gravitational force acting on.

00:36 So for part a adding on the particle a.

00:44 So we know that the gravitational force is an attractive force.

00:53 So the particle a feels attracted to the particle b and c.

01:02 So let's call that the force a over b.

01:07 And force a c over a, okay? then the resulting force in here, it's called this the force in a, is, well, in magnitude, is equal to, well, the sum of these two forces, okay? so that will be the force of b over a plus the force on a and of c over a.

01:40 Okay.

01:40 And now we use the definition of the gravitational force, which is the gravitational constant, the gravitational constant, times the product between the masses, this divided by the separation distance to the square.

01:55 Okay, now we're going to call the separation distance between a and c as the distance art a, c, and the separations between a and b as art a, b.

02:11 So rac is equal to 0 .5 plus 0 .25.

02:17 So that will be 0 .75 in units of meters.

02:22 And the radios ab is just simply 0 .5.

02:29 Now with that said, let's just substitute that definition in here.

02:34 Now both in this case points to the right, okay? so they point in the same.

02:43 So that will be the gravitational force.

02:47 We can take that out as a constant.

02:49 We can also take out the mass of a.

02:52 Then we will have the just simply in here, the mass of b divided by the separation a and b through the square.

03:01 This plus the mass of c divided by the radius between a and c and that to the square.

03:11 So i'm going to substitute the values.

03:13 I'm going to leave you to you to determine these magnitude.

03:17 Okay, so the gravitational constant g is 6 .67 times 10 to the minus 11.

03:24 The mass of a is given, and that will be 363 kilograms.

03:30 The mass of b also given, that is 517, divided by the separation distance a, b, that is equal to 0 .5, and that to the square.

03:42 This plus the mass of c, that is 100 ,000.

03:46 And 54 divided by the separation distance between a and c, that is 0 .75, and that to the square.

03:59 Then you can just use the calculator...

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