Normal Force
Overview
The normal force is always perpendicular to the contact surface — it is a contact force from the surface pushing back. It adjusts to maintain equilibrium in the perpendicular direction. On a flat surface: N = mg. On a slope: N = mg cosθ. In a lift accelerating upward: N = m(g + a). In free fall: N = 0 (weightlessness).
What is normal force?
The normal force N is a contact force exerted by a surface on an object, always perpendicular (normal) to the surface. It arises from the electromagnetic repulsion between surface atoms. The normal force adjusts to prevent objects from passing through each other. On a flat surface for a stationary object, N = mg. But N is NOT always equal to mg — it depends on all other vertical forces and any vertical acceleration.
When does N ≠ mg?
N ≠ mg when: (1) The surface is inclined (N = mg cos θ). (2) There is vertical acceleration (N = m(g ± a)). (3) An additional vertical force is applied (pushing down increases N; pulling up decreases N). (4) The object is on a curved surface moving in circular motion. In a lift accelerating upward: N = m(g + a). In a lift accelerating downward: N = m(g − a). In free fall: N = 0 (apparent weightlessness).
- ⚠Always setting N = mg without checking if there's acceleration or incline
- ⚠Confusing deceleration while going up (acceleration downward) with acceleration while going down