Question

A 100m cable hangs in a deep well and is attached to a suspended container that has a mass of 10kg. If the cable is 200kg in total, what is the work done in pulling the container to the top of the well?

Answer 1

I'm not sure what the answer is going to be going in, but hopefully we can figure it out.

Since we know W=Fd, we obviously need to look for what our distance and force is going to be. I'm willing to assume that the force will be gravity and the distance will be the whole length of the cable. But as we pull in this thing, it'll weight less and less. So basically, let's find a formula for force of gravity with respect to time or length or something.

Answer 2

We have to treat the cable and container separately.

Answer 3

Yeah, so I'm thinking the cable mass density is like our slope and the container is like our y-intercept sort of thing going on.

Answer 4

\[mass = \frac{ 200 kg }{ 100 m }*length + 20 kg\]

Answer 5

Errr... Yeah that's wrong, 10kg not 20.

Answer 6

multiply that by 9.8 m/s^2 and an infinitesimal displacement dx, add up all of those from 0 to 100 meters and I think your answer is revealed?

Answer 7

Yeah I think that's right..haha. I actually don't have the answer.

Answer 8

It feels pretty right, I'll do the calculation real quick and I'll check your answer to see if we got the same thing at the very least.

Answer 9

I ended up with the same integral

Answer 10

So you were just checking to make sure someone else could independently come up with the same integral? Sounds good to me, doubt we're both wrong lol.

Answer 11

Yup :)

Answer 12

AT first I treated the cable and container as a singular object, which got me an odd answer, so that's why I redid it and thought I'd post it to make sure I did it correctly this time.

Answer 13

Ahh, so you did the rope separately from the bucket? I suppose that would work since they're just a linear combination. Interesting.