I had a homework problem with this graph of F(Newtons) vs x(meters).
The graph has a straight line (constant slope) from (0,0) to (8,10).
And the slope ((10-0)/(8-0)) came out to be 1.25, making the function of the graph be F = 1.25x.
Then the question was to find the "Work done by force during the displacement".
Which is to simply take integral of and plugging in the numbers.
Integral came out to be 0.625x^2.
To find the area under curve from 0 to 8 meters (Work done by force during displacement from 0 to 8 meters),
I just plugged in 8 meters into the function and the number came out to be 40.
However I'm not quite sure about what the unit is for this problem.
It HAS to be Joules (N*m).
But I'm not sure how I should reformat/move around to make the unit be N*m.
Is there any proof on this?
Best Answer
The slope you calculated is $\frac{10 \rm N}{8\rm m}=1.25\,{\rm \frac Nm}$, so the force function becomes $F=1.25\,{\rm \frac Nm}*x$. Hence, the work is $$ W=\int{(1.25\,{\rm \frac Nm}\times x)dx}=1.25\,{\rm \frac Nm}\int{xdx}=0.625\,{\rm \frac Nm}x^2 $$ (If $F(0)=0$). Because the unit of $x^2$ is $\rm m^2$, then the unit of the work is, as expected, $\rm N/m\times m^2=N*m$