Gravitational Field Problem - Integrate?

Mmm_Pasta

1. The problem statement, all variables and given/known data
A nonuniform thin rod of length L lies on the x axis. One end of the rod is at the origin, and the other end is at x = L. The rod's mass per unit length λ varies as λ = Cx, where C is a constant. (Thus, an element of the rod has mass dm = λdx.)

Determine the gravitational field due to the rod on the x axis at x = x0, where x0 > L. (Use the following as necessary: G, M, L, x0.)


2. Relevant equations

F=GMm/d^2
g=GM/d^2

3. The attempt at a solution
Since the mass varies depending what L is, the equation would be Gdm/(x₀-L)^2 which is Gλdx/(x₀-L)^2. Do I then integrate to get rid of the dx? If I do I am not sure what dx would be to begin with.

cepheid

This looks close, although I think it should be (x₀ - x)² in the denominator, since you are talking about the contribution due to the infinitesimal mass element located at position x.

What do you mean by "I don't know what the dx would be to begin with?" Do you know calculus?

Mmm_Pasta

I put L because x₀ is greater than L, but now I know why it is x. Never mind about the dx; I worded the question wrong, but I know now. Thanks. =)