Finding the Weight of a Rope and Bucket

[glennpagano]

Homework Statement

A rope is 5 meters long and hangs over the edge of a well. It has a bucket of water weighted 20 kilograms attached to one end. For Simplicity, use g=10N/kg

Suppose the rope has a uniform density of $$\rho$$ = 1kg/m

Homework Equations

W=$$\int$$ F(x)xdx

The Attempt at a Solution

I could not figure out what the force would be I would think it would be (Mrope+Mbucket)g
Mass of the rope would be ($$\rho$$)(v)=Mrope

 

[tiny-tim]

Welcome to PF!

Welcome to PF!

(have a rho: ρ and an integral: ∫ )

Does the question ask for the work done in raising the bucket 5 m ?

If so, remember that the rope doesn't rise 5 m … it stops as it gets to the top.

Use work done = change in PE.

 

[glennpagano]

I know I can do change in PE but this is for my calculus and my teacher wants me to use calculus I did some more work and found this so far. F(y)=(Mrope+Mbucket) Mrope=$$\rho$$v. Now I have to find change in y for that I got (5-y) Now my equation for work is the integral from 0 to 5 of ($$\rho$$y+20)(5-y)