- #1
teroenza
- 195
- 5
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.
Homework Equations
F=-G*(M*m)/R^2 (times radial unit vector rhat for the vector form)
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?
Last edited: