Question

describe how you would determine the force acting on an object if the forces were not acting in the same direction?

Explanation:

Step1: Resolve forces into components

Resolve each non - parallel force into its x and y (or other appropriate coordinate system) components. For a force $\vec{F}$ with magnitude $F$ and angle $\theta$ with the x - axis, the x - component is $F_x = F\cos\theta$ and the y - component is $F_y = F\sin\theta$.

Step2: Sum the components

Sum all the x - components of the forces to get $F_{netx}=\sum F_x$ and sum all the y - components of the forces to get $F_{nety}=\sum F_y$.

Step3: Calculate the net force magnitude

Use the Pythagorean theorem to find the magnitude of the net force $F_{net}=\sqrt{F_{netx}^2 + F_{nety}^2}$.

Step4: Determine the direction

Use the inverse - tangent function to find the direction of the net force $\theta_{net}=\tan^{- 1}(\frac{F_{nety}}{F_{netx}})$.

Answer:

First, resolve non - parallel forces into components. Then sum the components in each direction. Calculate the magnitude of the net force using the Pythagorean theorem and find its direction using the inverse - tangent function.