# How mush work is done in lifting a 40 kilogram weight to a height of 1.5 meters?

Aug 21, 2014

The answer is $588 J$.

$W = {\int}_{a}^{b} F \left(x\right) \mathrm{dx}$

Sometimes, the simple problems are the hardest because it looks too easy so we tend to add unnecessary things. Since this is a vertical lift, we are dealing with gravity which is 9.8 $\frac{m}{s} ^ 2$. So,

$F \left(x\right) = 9.8 \frac{m}{{s}^{2}} \cdot 40 k g = 392 N$

Remember that work is force times distance. We have force which is just a constant function. And we have distance which is $\mathrm{dx}$. The tendency is to add an $x$ into $F \left(x\right) = 392 N$, but that would be incorrect. Now, let's put it together:

$a = 0$
$b = 1.5$
$W = {\int}_{0}^{1.5} 392 \mathrm{dx}$
$= 392 x {|}_{0}^{1.5}$
$= 588 J$