Question

Please help me with this homework question if possible! thank you so much

Answer 1

a. 2, south

b. 2, north

Explanation:

With the help of graphing, we can determine the magnitude of each force.

We must bear in mind that in the case of forces F2 and F3. both are divided into their x component and their y component.

The sum of force on the x-axis would be:

`\begin{gathered} \sum ^{}_{}F_x=F_1+F_(2x)+F_(3x)_{}_{} \\ \text{ We replacing} \\ \sum ^{}_{}F_x=(-3)+(-1)+4_{}=-4+4 \\ \sum ^{}_{}F_x=0 \end{gathered}`

The sum of force on the y-axis would be:

`\begin{gathered} \sum ^{}_{}F_y=F_(2y)+F_(3y)+F_4 \\ \text{ We replacing} \\ \sum ^{}_{}F_y=4+(-2)+(-4)_{}=4-6 \\ \sum ^{}_{}F_y=-2 \end{gathered}`

Since the sum in x is equal to 0, the resulting force would be:

`F_R=2,\text{ south}`

Therefore, for it to be in equilibrium, a force must be added in the opposite direction but in the same magnitude as the resulting force, which would be:

`F=2,\text{ north}`