A rod, a ball, garvitational Potential Energy (U), and the power series expns.

[TFM]

Homework Statement

Mass of rod: M
mass of ball: m
Length of Rod: L
distance between rod and ball: x
GPE is zero at infinty

The questiopn asks to take the GPE of the rod/ball system, using the Power Series Expansion for ln(1+x) .

Homework Equations

U = -GMm/r

The Attempt at a Solution

I'm not quite sure where to start - the Power Series expansion has confused me slightly, as otherwise I wouold hqave just put the variables in the above equation?

TFM

 

[awvvu]

It just means you can approximate ln(1+x) with x, for x << 1.

 

[TFM]

Where does the Ln(x+1)come from?

TFM

 

[awvvu]

It'll probably appear as you solve the problem. They say to use the power series to make it easier to solve.

 

[TFM]

Do you still use the U=-GMm/r, with U = 0, r = infinty, giving:

0=-GMm/infinity?

TFM

 

[SpitfireAce]

I guess you want to integrate over the length of the rod and end up with the integral of
(1/l+1) dl from 0 to L... that should give you ln(x+1)

U= -GmM/L [integral 0 to L (dl /sqrt. of x^2+l^2)] and I guess you can say that the square root of x^2+l^2 is x+C where C is some constant, though this makes no sense I can't think of any other way

btw, the way I got that is by saying dU= -Gm(dM)/r.. then setting dM=dl(M/L) and r=sqrt. (x^2+l^2)

 

[t-money]

take the intergral of 1/r, which is ln(r), setting your limits from infinity to x. Do you know the expansion to ln(r)?

 

[SpitfireAce]

from infinity to x? how in the world do you integrate from infinity to x?

 

[TFM]

take the intergral of 1/r, which is ln(r), setting your limits from infinity to x. Do you know the expansion to ln(r)?

Why do I need to take the integral of 1/r?

TFM

 

[TFM]

I'm Still rather cionfused about what I should be doing

Any Help?

TFM