Work: Compute the amount of work done in lifting 100 lbs

[Guest]

Compute the amount of work done in lifting a 100 lb weight a height of 10 ft assuming that this work is done against the constant force of gravity.

I have to use the equation W = integral F(x) dx, but I'm not really sure how to use it. I don't understand why we can't just use Work = Force* distance.

 

[galactus]

The idea is the same as the tank problem. The force required to move the kth layer equals the weight of the layer.

In this case, it's foot-lbs. So, multiply 10(100-x). See?.

\(\displaystyle \L\\\int_{0}^{10}100(10-x)dx\)

 

[daon]

An integral is not necessary here. Note that 100lbs IS the force, and already takes gravity into consideration.

W = f*d
W = 100lbs * 10ft = 1000 ft*lbs of work

To write as integral,

W = \(\displaystyle \L \int _0^{10} 100 dx\)

 

[galactus]

Yes, I erred. Daon is correct.

My way is as if the problem stated "how much work is required to lift, say,

a chain weiging 100 lbs/ft a height of 10 feet".

That's one big chain. Maybe for a ship's anchor. :lol: