Two gravitational force questions

[psruler]

Can someone help me with these two questions:

a. Imagine two spherical planets fixed on the x-axis, one with mass M at the origin, and the other with identical mass M at the position x = +100.0 units. At what position along the x-axis between the two masses could you position yourself so that you would experience a net gravitational force of zero? (I.e., at what x-position do the two gravitational force vectors acting on you exactly cancel? YOU do NOT need to show your work for this part.)

b. Now imagine a similar arrangement of two planets, but with a mass of 4M at the origin. Again, at what position along the x-axis between the two masses would you experience a net gravitational force of zero? Show your work.

THANKS!

 

[outandbeyond2004]

I assume these two bodies are the only ones around.

By symmetry, 50 units of distance on the x-axis from the origin in between the bodies.

As for the second question, do you understand what to do?

-$$\frac{GM}-r[\tex]<br /> where r is the distancefrom one body to the point in question.$$

 

[psruler]

Well, i don't quite understand the second question. Did you give me a formula? If so, i don't understand it.

 

[paul11273]

You should have the formula somewhere in your text or lecture notes for the gravitational force created by a body:

Fg=G(m/r^2)

Where Fg is the graviational force
G is the gravitational constant (a value that should also be in your book, although in this question you see that G cancels out of the equation you set up.)
m is the mass of the body
r is the distance to the point where you are calculating the gravitational force.

For your second question, you are given the distance between the two planets, 100 units.

You should understand that you are looking for a point somewhere between them so that the gravitational forces cancel each other...in other words, they are equal magnitude in opposite directions (HINT, HINT)

That will be some distance (r in the equation) from each one. Let one distance be x, and the other be 100-x.
Set up the two equations equal to each other, and solve for x.

Post up some work so we can take this further and see where you get stuck.

 

[psruler]

so for qestion 2, do i use the gravitatinal force equation? and then somewhere in the equation i have x and x-100

 

[paul11273]

Yes, use the gravitational force equation. You will write one formula for each gravity, one for the 4m mass and one for the m mass.
The point lies somewhere between them. Start with a diagram, and show that the distance is 100. Now designate some portion of the distance as x. It doesn't matter which portion or how much. That which is left over is defined as 100-x.

The distances x and 100-x are the radius r in each formula. Set these two formula's equal to each other and solve for x.

G(4m/(100-x)^2) = G(m/x^2)

The G cancels on each side.

4m/(100-x)^2 = m/x^2

Cross multiply and solve the quadratic equation for x.

 

[outandbeyond2004]

I am sorry! I was editing the message when I got interrupted.

 

[psruler]

Ok this is what i got so far: 4Mx^2 = (10000-100x+x^2)M. now do i have to solve for x? btw, is 4M, 4 * mass?

 

[paul11273]

4Mx^2 = (10000-100x+x^2)M

You are on track except you should have -200x instead of -100x.

Yes, 4M is 4 * Mass.

Now solve for x.