Work: Emptying a 2x1x1 box of water.

[TylerH]

Homework Statement

How much work is required to empty a 2x1x1 ft box of water? Assume density of water is 62.5 lb/ft³.

Homework Equations

$$\int_a^b A(x)xdx$$
$$A(x)=lw=2$$

The Attempt at a Solution

$$62.5\int_0^1 2xdx=125\left[ \frac{x^2}{2} \right]_0^1=62.5$$

Did I get it right?

 

[Whitishcube]

looks good to me. Although if I were to give advice, I would say don't try to memorize those kinds of formulas. Instead, try to remember a method for setting these types of problems up. Usually this involves some form of considering a small "slice" of water of width $\Delta x$ and finding the small amount of work $\Delta W$ and then summing up over the entire volume of the water.
this method might seem tedious for simple problems, but it might give you a better understanding of what is really going on here.

 

[TylerH]

Yeah, I know exactly what you mean. The whole point of covering work is to solidify the concept of the integral being an infinite sum of infinitesimals. I didn't show or explain my derivation, but I didn't memorise the formula, as it appears.

I was just wondering, because this was a question on a test and I was beginning to believe I missed it. I'll see for sure tomorrow (Monday).