Answer
$F_{right}=\fbox{22.89 N}$
$F_{left}= \fbox{16.34 N}$
Work Step by Step
We first integrate the function:
$= \int_0^2 (1+x) dx = 4 $
We now integrate the function times x:
$= \int_0^2 (x+x^2) dx = 4.67$
We now divide these two values to find the center of mass:
$CM = 1.167$
Thus, we find the values of the scale readings to find what value will make the torque 0 to obtain:
$1.167F_{left}=.833 F_{right}$
$F_{left}=.714 F_{right}$
We now use the fact that the scales add to the force of gravity to find:
$F_{left}+F_{right}=4(9.81) $
$.714 F_{right}+F_{right}=4(9.81) $
$F_{right}=\fbox{22.89 N}$
$F_{left}=22.89 \times .714 = \fbox{16.34 N}$
