In Fig. 13-41, a particle of mass m1 = 0.23 kg is a distance d = 84 cm from one end of a uniform rod with length L = 6.4 m and mass M = 2.4 kg. What is the magnitude of the gravitational force on the particle from the rod?
The Attempt at a Solution
ok...so i figured that the desnity of the rod, M/L should be the same for dm/dr...so then dm=(M/L)dx. (i thought just to visualize easier i made dr into dx, so it looked like a coordinate system to me)
then i figured i had to integrate F=int (dF)
so i did F= int (Gmdm)/(x+d)^2...since dm=(M/L)dx this made the integral
further simplifying i got F= (GmM/L) integral dx(x+d)^2
after integration i got F= GmM/L multiplied by -(x+d)^-1 from 0 to L...
then i solved, etc. but got the wrong answer...any idea if this is totally off or if i made a silly mistake somewhere?