It is interesting that you can find the total or net work done using the much easier kinetic energy approach.
Due to total energy being conserved, it's like a yo yo (harmonic oscillator). The mass starts at speed of zero, and accelerates as it goes down the tunnel because the Earth is pulling on...
ok so finding the net work using the gravity approach should come out to the same answer using the kinetic energy approach.
So you will have
##\int\limits_{-r}^{r}\frac{w}{r}xdx =0##
and the kinetic energy will be the same 0 speed at top and bottom ##\frac{1}{2}mv^2## gives us zero when...
that makes sense, dimensional analysis gives me ##mi*lb## or ##ft*lb## by multiplying by 5280.
As for your second reply does negative work make sense, i guess it does if you account for direction and choose up as positive.
If you allow for negative work, then the work should come out to zero...
Homework Statement
The force of attraction on an object below Earth's surface is directly proportional to it's distance from Earth's center.Find the work done in moving a weight of ##w## lb located ##a## miles below Earth's surface up to the surface itself. Assume Earth's radius is a constant...
Have you looked into khanacademy.org ? they have videos on all basic high school math (rules of fractions) up to college math (multivariable calculus and linear algebra). This will fill in many of the gaps or holes in your math education.