multiple choice question\nthe free - body diagram of an object is shown. select the vector that best…

Explanation:

Step1: Resolve forces into components

Resolve $F_1$, $F_2$, $F_3$, $F_4$ into $x -$ and $y -$ components. Assume each grid - square represents a unit of force. Let's say $F_1$ has components $(F_{1x},F_{1y})$, $F_2=(F_{2x},F_{2y})$, $F_3=(F_{3x},F_{3y})$ and $F_4=(F_{4x},F_{4y})$. From the diagram, if we assume $F_1$ has a positive $x$ and positive $y$ component, $F_2$ has a negative $x$ component and zero $y$ component, $F_3$ has a zero $x$ component and negative $y$ component, and $F_4$ has a zero $x$ component and positive $y$ component.

Step2: Calculate net $x -$ component of force

$F_{netx}=F_{1x}+F_{2x}+F_{3x}+F_{4x}$. Since $F_2$ is in the negative $x -$ direction and $F_1$ has a positive $x -$ component and $F_3,F_4$ have zero $x -$ components, $F_{netx}=F_{1x}-|F_{2x}|$.

Step3: Calculate net $y -$ component of force

$F_{nety}=F_{1y}+F_{2y}+F_{3y}+F_{4y}$. $F_{2y} = 0$, $F_{3y}<0$, $F_{4y}>0$ and $F_{1y}>0$. So $F_{nety}=F_{1y}+F_{4y}-|F_{3y}|$.

Step4: Determine direction of net force

The direction of the net force $\vec{F}{net}$ is given by $\theta=\tan^{- 1}(\frac{F{nety}}{F_{netx}})$. By visual inspection and rough - calculation of components, we can see that the net force has a positive $x$ and positive $y$ component.

Answer:

b