Calculating Work via Integration Video Lessons

Concept

# Problem: A heavy rope, 50 ft long, weighs 0.5 lb ft and hangs over theedge of a building 120 ft high.(a) How much work is done in pulling the rope to the top ofthe building?(b) How much work is done in pulling half the rope to the topof the building?

###### FREE Expert Solution

(a)

The total work is given by:

$\overline{){\mathbf{W}}{\mathbf{=}}{\mathbf{\int }}{\mathbf{F}}{\mathbf{\left(}}{\mathbf{x}}{\mathbf{\right)}}{\mathbf{d}}{\mathbf{x}}}$

Let's divide the rope into pieces of length Δx

The portion of the rope from x ft to Δx ft below the top of the building has a weight of 0.5 ft/lb.

This portion must be moved x feet.

Therefore, the total work is given by:

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###### Problem Details

A heavy rope, 50 ft long, weighs 0.5 lb ft and hangs over the
edge of a building 120 ft high.
(a) How much work is done in pulling the rope to the top of
the building?
(b) How much work is done in pulling half the rope to the top
of the building?