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.
Physics - drwls, Thursday, December 11, 2008 at 11:08am
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