Question

A chain 27 feet long whose weight is 95 pounds is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the entire chain to the top of the building?

Answer 1

Answer:

Work done $= 2,565$ lb-ft

Step-by-step explanation:

The density of the chain in lb/ft  is equal to

$\frac{95}{27}$ lb/ft

Total Work done is equal to the summation of  work done up to the top of building.

We will use integration for this evaluation.

The mathematical relation is as follows

$\int\limits^{40}_0 {X} \, pdx$

where "p" is the density

Substituting the given values, we get

$\frac{95}{27} \int\limits^{27}_0 {X} \, dx\\\frac{95}{27} X^2\int\limits^{27}_0\\ \frac{95}{27} {27^2 - 0^2}\\\frac{95}{27} * 27 * 27\\95* 27\\= 2,565$

Work done $= 2,565$ lb-ft