Calculating Gravitational Force on a Point Mass in a Semicircular Rod

[pete06]

A uniform rod of mass M = 20kg and length L = 5m is bent into a semicircle. What is the gravitational force exerted by the rod on a point mass m = 0.1 kg located at the center of curvature of the circular arc?

 

[pete06]

I have assumed that this must be solved using the summation of all points on the rod since each exerts its own force on the point mass. Assuming that to be true, I figured that the x components all cancel each other out, leaving only the y components. But now, I don't know how to solve this?

 

[OlderDan]

You are on the right track. You have the symmetry figured out. Break the rod up into bits of mass dm and write the y component of the force related to each bit of mass. Add all the y components (integrate over the masses). This is most easily done by converting to an integral over an angle.