كيفية الحساب القوة العمودية (N = mg and mg cosθ): الصيغة & Examples
احسب normal force with N = mg on a floor and N = mg cosθ on a ramp. See when a push or lift changes N, then verify every answer with a free normal force calculator.
What القوة العمودية Means
Normal force is the support force a surface exerts on an object, perpendicular to the surface. A floor pushes up; a ramp pushes at right angles to the slope. It is not a new kind of force — it is whatever contact force is needed so the object does not sink into the surface.
The most common homework trap is writing N = mg on every problem. That is true only on a horizontal surface with no other vertical forces. Tilts, pushes, lifts, and elevators all change N.
If you already have mass, angle, and g and only need a checked number, open the free normal force calculator first, then return here for the flat-vs-ramp distinction and worked examples.
The الصيغةs N = mg and N = mg cosθ
θ = 0° recovers the flat-floor case because cos(0°) = 1. As the ramp steepens, cosθ falls and N drops.
Units That Keep Marks Safe
الشغلed Examples
Example 1: 5.0 kg on a flat floor
g = 9.8 m/s², no extra force. N = (5.0)(9.8) = 49 N upward. The floor pushes up 49 N; the block pushes down on the floor with 49 N.
Example 2: same mass on a 30° ramp
N = mg cos(30°) = 49 × 0.866 ≈ 42.4 N, perpendicular to the ramp. Using N = 49 N here would also break any friction calculation that needs μN.
Example 3: 20 N downward push
A 2.0 kg box on a table, g = 9.8, plus a 20 N downward push. N = 19.6 + 20 = 39.6 N. An equal upward lift would make N negative — contact is lost and the box leaves the table.
القوة العمودية vs الوزن vs الاحتكاك
الوزن mg always points toward Earth’s centre. Normal force is set by the surface direction. الاحتكاك is usually along the surface and sized from N: Ff = μN. Get N wrong and friction follows it.
For ramp acceleration and μ_min = tanθ, see how to solve inclined plane problems.
أخطاء شائعة
Sanity check: on a ramp, N should be smaller than mg, not larger, unless something extra pushes into the surface.
Check With the مجاني Calculator
Normal force calculator — flat floor, ramp, or extra vertical force.
Inclined plane calculator — a, F∥, N, and μ_min together.
الاحتكاك calculator — Ff = μN.
الوزن calculator — W = mg before you resolve components.
Learn N = mg versus N = mg cosθ, then confirm every answer on the calculator.