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**1. Homework Statement**

Infinitely long rod with the z axis at its center. The rod has a uniform mass per unit length [itex]\mu[/itex]. Find the gravitational force vector

**F**on a mass m, at a distance [itex]\rho[/itex] from the z axis.

**2. Homework Equations**

**F**=-G*(M*m)/R^2 (times radial unit vector rhat for the vector form)

**3. The Attempt at a Solution**

I believe I can treat the rod as being very thin, with a center of mass along the z axis. Then I labeled the masses position as being on the y axis. I believe that the force exerted on m in the z direction cancel because of symmetry. I believe I need to work in cylindrical polar coordinates because of the problems use of [itex]\rho[/itex] and z.

I do not see how to construct an integral (from - infinity to + infinity) in polar coordinates. I know I need to vary z. I tried to construct an equivalent integral in Cartesian coordinates as follows.

-G[itex]\mu[/itex]m[itex]\int[/itex]dz/(y^2+z^2)

G is the gravitational constant.

integral from -infinity to infinity

M= mass of 2nd object in Newton's law of gravitation was replaced by [itex]\mu[/itex]*z

r= distance from z axis= (y^2+z^2)^1/2

y is a constant because the mass is always a the same y position.

But I think this is wrong. Can someone help?

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