# Physics problem

• Dec 28th 2005, 10:20 PM
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
• Dec 28th 2005, 10:45 PM
rgep
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.
• Dec 28th 2005, 11:23 PM
CaptainBlack
Quote:

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