Gravitation, really hard at least for me

[Puchinita5]

Homework Statement

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?

Homework Equations

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c13/fig13_41.gif

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
int (GmMdx)/L(x+d)^2

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?

 

[queenofbabes]

It looks correct...

 

[turin]

It looks correct to me, too. However, I would just make a comment on your integral: you should be more explicit about the limits. E.g. I did a change of variables that changed my limits to d and L+d (but anyway I got the same result as you).

Maybe you just forgot to convert cm to m?

 

[Puchinita5]

i'm an idiot... the answer was about 6.05e-12, and when i plugged it into the website i left out the e-12...what a silly mistake! well, i have looked at it sooo many times at least that i will never forget how to do this problem...