Practice

N = mg cosθ Formula – Normal Force Practice

N = mg cosθ — Flat: N = mg; incline: N = mg cosθ

The normal force is the support force perpendicular to a surface. On a flat floor N = mg; on an incline N = mg cosθ.

Guide — how to use this formula

1. 1. Flat rest: N = mg.
2. 2. Ramp: N = mg cosθ (not mg).
3. 3. Upward lift reduces N; downward push increases N.
4. 4. Friction often uses Ff = μN after you find N.

Derivation

Resolve weight perpendicular to the surface:

1. Flat surface (θ = 0):
   N = mg
2. Incline at angle θ:
   N = mg\cos\theta

θ is the angle between the surface and horizontal; cos 60° = ½.

Examples

Example: flat 5 kg

g = 10 → N = 50 N.

Example: 60° ramp

N = ½ mg.

Practice on the interactive page

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