A steel girder weighing $200 \mathrm { lb }$ is hoisted from ground level to the roof of a 40 -ft building using a chain that weighs $5 \mathrm { lb } /$ running foot. Find the work done.

Question

Quizplus · Accepted Answer

The work done is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force applied is the weight of the steel girder, which is 200 lb. The distance over which the force is applied is the height of the building plus the length of the chain. The length of the chain is not given, but we can calculate it by noting that the chain weighs 5 lb per foot, and therefore the total weight of the chain is 5 times the length of the chain in feet. Letting x be the length of the chain in feet, we have:

weight of chain = 5x lb

total weight lifted = weight of girder + weight of chain
                                  = 200 + 5x lb

distance lifted = height of building = 40ft
Therefore, we can find the work done as follows:

work done = force x distance
                    = (200 + 5x) lb x 40 ft
                    = 8,000 lb-ft + 200x ft-lb

To find the value of x that maximizes the work done, we can take the derivative of the work done with respect to x and set it equal to 0:

d(work)/dx = 200 ft-lb = 0
                x = 40

Therefore, the length of the chain is 40 feet, and the work done is:

work done = 8,000 lb-ft + 200(40) ft-lb
                    = 12,000 ft-lb

So the answer is C, $12,000 \mathrm { ft } - \mathrm { lb }$.

A Steel Girder Weighing 200lb200 \mathrm { lb }200lb Is Hoisted from Ground Level to the Roof of a Hoisted

A Steel Girder Weighing $200 \mathrm { lb }$ Is Hoisted from Ground Level to the Roof of a Hoisted