Resultant (net) force

1. What is Resultant Force?

When multiple forces act on an object, the resultant force is the vector sum of all forces.
Formula: $F_{res} = F_1 + F_2 + F_3 + ...$

(taking direction into account)

If forces act in the same direction, add them.
If forces act in opposite directions, subtract them.
If forces act at an angle, use vector components and the Pythagorean theorem where needed.

infoNote

Forces acting on a box on a horizontal surface:
Applied force $(F_{app})$$:$ 100 N (right).
Friction force $(F_f):$ 55 N (left).
Normal force $(F_N)$ : Perpendicular to the surface.
Weight $(F_g):$ Acts downward.
Resultant force calculation: $F_{res} = F_{app} - F_f = 100 - 55 = :highlight[45 N] \text{ (to the right)}$

infoNote

Forces acting:
Weight $(F_g)$ , broken into:
Parallel component $(F_g \sin \theta):$ Pulls the object down the slope.
Perpendicular component $(F_g \cos \theta):$ Presses the object into the surface.
Friction force $(F_f)$ : Opposes motion up the slope.
Resultant force calculation: $F_{res} = (mg \sin \theta) - F_f$
$If$ $m=$ 100 kg, $g=$ 9.8 m/s², $θ=$ 30°, and $F_f =$ 20 N: $F_{res} = (100 \times 9.8 \times \sin 30^\circ) - 20 = :highlight[470 N] \text{ (down the slope)}$

Forces between charged spheres follow Coulomb's Law.
If charges are opposite, the force is attractive.
If charges are the same, the force is repulsive.
Example Calculation:
- Two forces act on a charged sphere, +450N (left) and +350N (right).
- Using vector addition: $F_{res} = \sqrt{450^2 + 350^2} = :highlight[570 N]$