Maximum Force on a Test Mass in a Massive Ring

[kraigandrews]

Homework Statement

A massive ring (radius = a and mass = M) lies on the xy plane. Calculate the force F on a test mass m at position z on the z axis.
Now assume a = 1 and GMm/a2 = 1 in some system of units.

(a) What is the force on m at z = 0?
I got the answer for this its 0
(b) What is the force on m at z = a?
the answer for this is 0.354
(c) What is the maximum force on m ?
I am stuck on this one.

Homework Equations

F=(GMm)/r^2

The Attempt at a Solution

after some work I get F=(2GmMx)/(x^2+a^2)^3/2
i know this is right because i got part b from it, however i don't Know how to find the maximum, my gut feeling is take the derivative with respect to x and set it equal to zero and then solve for x and plug back into F

 

[gneill]

after some work I get F=(2GmMx)/(x^2+a^2)^3/2
i know this is right because i got part b from it, however i don't Know how to find the maximum, my gut feeling is take the derivative with respect to x and set it equal to zero and then solve for x and plug back into F

I'm not sure where that "2" comes from in your force expression. Better check that derivation.

And yes, you need to differentiate and solve as you've outlined.