There is a horizontal rod of length L and mass M. A point mass m is vertically above the rod at a vertical distance L/4 and horizontal distance L/3 from one end of the rod.Using The Riemann sum Integral,find the magnitude and direction of the gravitational force exerted on the point mass by the rod.
Write the expression for the vertical and horizontal components of the gravoty force. It will require an integration along the length of the rod.
The vertical force component is
G*m*(M/L)*dx*(L/4)/[(L/4)^2 + x^2]^3/2
integrate that from x=0 to x = L
The messy looking denominator is the cube of the distance between mass m and dx. You need a cube instead of a square becasue you need to include a cosine term for the vertical component. For the horizontal force, you will have a different integral beasue you need a sine term.
Doing this with Riemann sums is rather messay and I will leave that you you or another teacher