First case forces in the same direction
[tex]F=30+40=70N[/tex][tex]F=ma[/tex]
We isolate the a
[tex]a=\frac{F}{m}[/tex]
Then we substitute the data
[tex]a=\frac{70}{20}=3.5m/s^2\text{ }[/tex]
Second case
[tex]F=40-30=10N[/tex][tex]a=\frac{10}{20}=\frac{1}{2}=0.5m/s^2[/tex]
Third case
[tex]F_x=40N[/tex]
[tex]F_y=30-W[/tex]
The weight W is
[tex]W=20\cdot9.8=196N[/tex][tex]F_y=30-196=-166[/tex][tex]R=\sqrt[]{40^2+(-166)^2}=170.75N[/tex][tex]\theta=\tan ^{-1}\frac{-166}{40}=-76.45\text{\degree}[/tex][tex]a=\frac{F}{m}=\frac{170.75}{20}=8.5375m/s^2\text{ at -76.45\degree}[/tex]
