Forces that cancel out

Recognizing the balance of forces

To apply the principle of inertia, you must first list the forces acting on a system, then check whether their vector sum is zero: sum F = 0 vector. The system is then said to be in equilibrium, or pseudo-isolated.

Method in 3 steps

1. Precisely define the system under study (the object).
2. List the external forces acting on it (weight, normal reaction from the support, tension in a string, friction, buoyancy...).
3. Calculate or graphically represent the sum of the forces. If sum F = 0 vector, then according to the principle of inertia, the object is at rest or in uniform rectilinear motion in a Galilean frame.

Numerical example

A crate of mass m = 20 kg slides at constant speed on a horizontal floor, pulled by a force F = 40 N. The weight P = mg = 209.8 = 196 N (with g = 9.8 m/s^2) is balanced by the normal reaction N from the floor (N = 196 N). Since the speed is constant, the driving force F is necessarily balanced by friction f, so f = F = 40 N.

Force	Value (N)	Balanced by
Weight P	196	Normal reaction N
Driving force F	40	Friction f

Key takeaway

Constant speed does not imply the absence of forces, but their exact cancellation. This is a frequent confusion: "no force, so at rest" is false; it is "sum of forces equal to zero" that gives rest OR uniform rectilinear motion.