Net Force Summation
States that the net force on an object equals the vector sum of all individual forces acting on it
The equation
What it solves
States that the net force on an object equals the vector sum of all individual forces acting on it. This net force then determines the acceleration via Newton's second law.
When to use it
Every classical mechanics problem that involves more than one force. Begin by drawing a free-body diagram, then resolve all forces into components and sum each component axis separately.
When NOT to use it
The principle itself is always valid in an inertial frame. In non-inertial frames (accelerating elevators, rotating reference frames) you must add pseudo-forces. For systems of particles, apply it separately to each body.
Common mistakes
Including internal forces between parts of the same object — only external forces appear in ΣF. Forgetting to decompose angled forces into components before summing. Treating friction or normal force as automatically equal to weight without checking the actual geometry.
Topics that use this equation
Problems using this equation
- [medium] A 12 kg crate is pushed along a horizontal floor with a constant horizontal force of 80 N. The coeff…
- [hard] A 70 kg person stands on a bathroom scale inside an elevator. The elevator accelerates upward at 2.5…
- [challenge] Two masses are connected by a light inextensible string over a massless, frictionless pulley (an Atw…
- [exam] A 15 kg block is released from rest on a ramp inclined at 35° to the horizontal. The coefficient of …