Circular Motion - Satellites Problem

[Galileo_Galilei]

Homework Statement

Two satellites of equal mass, S1 and S2, orbit the earth. S1 is orbiting at a distance r from the Earth's center at speed v. S2 orbits at a distance 2r from the Earth's center at speed (v/squareroot2) . The ratio of the centripetal force on S1 to the centripetal force on S2 is,

A. 1/8

B. 1/4

C. 4

D. 8

Homework Equations

F = mvsqrd/r

The Attempt at a Solution

I just couldn't figure this one out at all... its frustrating, i tried playing around with the equation but i kept getting nonsense.

 

[Doc Al]

You have the correct equation. Show what you did to find F_1 and F_2 (the two centripetal forces).

 

[Galileo_Galilei]

Ok. So since the mass is equal its constant, so we just have

F = Vsquared/r

So then, S1 = Vsquared/r

S2 = (v/squareroot2)squared/2r
= (vsquared/2)/2r
= (2vsquared*r)/2


S1 = Vsquared/r

S2 = (2vsquared*r)/2


Hmm.. so now?

 

[mbrmbrg]

Ok. So since the mass is equal its constant, so we just have

F = Vsquared/r

Ultimately, that's all you need, but it would be more correct to leave the mass in until the very end.

So then, S1 = Vsquared/r

Right.

S2 = (v/squareroot2)squared/2r
= (vsquared/2)/2r
= (2vsquared*r)/2

Correcct until F_{S2}=m\frac{\frac{v^2}{2}}{2r}
Then you have an algebra error.

Hmm.. so now?

The problem asks you to take calculate a ratio, ie, divide one of the forces by the other. (Incidentally, that's why you can leave the mass in until the very end: both forces have the term 'm' so the masses cancel).

 

[Galileo_Galilei]

Oh, yeah, algebra got me there.

So it'd have to then be:

S2 = {\frac{v^2}{4r}}

Ah, so now it gives me a much simpler division to do. When i divide those S1/S2 after multiplying and cancelling i get 4r/r.

Awesome, so the answer is 4. Thanks for pointing out the algebra mistake.