# 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

Staff Emeritus
Gold Member
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.
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.

Do I then integrate to get rid of the dx? If I do I am not sure what dx would be to begin with.
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. =)

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