1. ## please check my work....

Question: A 100-ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building
Solution:
work = force* displacement

work = 15 lb/ft *100 ft

work = 1500 lb

2. No, because the part of the chain nearer the top doesn't have to be pulled so far. Also, your answer, being work, has to be in units of foot-pounds.

A link of the chain at distance x from the top and length dx weighs 15 dx pounds and is lifted x feet, so contributes 15x dx lb.ft to the work. Integrate to get $\displaystyle \int_0^{100} 15 x \; {\mathrm d}x$ as total work.

3. Originally Posted by bobby77
Question: A 100-ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building
Solution:
work = force* displacement

work = 15 lb/ft *100 ft

work = 1500 lb
Work also equals the change in energy. The mass of the chain is 1500 lb,
its initial centre of mass is at -50 ft (where we take the roof of the building
as our height reference point).

Now these are ridiculous units so lets convert them to the appropriate SI
units:

Mass $\displaystyle 1500 lb \equiv 680.4 kg$.
Length $\displaystyle 50 ft \equiv 15.24 m$.

Now the change in potential energy when the chain is at the top of the
building is $\displaystyle m.g.(h_{final}-h_{initial})\ \mbox{joules}$, where:
$\displaystyle g \approx 9.81 \ \mbox{m.s^{-2}}$,
$\displaystyle h_{initial}$ is the initial height of the centre of mass and
$\displaystyle h_{final}$ is the final height of the centre of mass.

So work done:

$\displaystyle WD\approx 680.4\times 9.81 \times 15.24\ \mbox{joules}\approx 101,722.8\ \mbox{joules}$,

or if you must about $\displaystyle 75,000 \ \mbox{ft-pounds}$ or $\displaystyle 73,576,000 \ \mbox{poundals}$

Of course if you are happier with customary units you can repeat the
calculation using them

RonL