계산 방법 수직 항력 (N = mg and mg cosθ): 공식 & 예제
계산 normal 힘 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 힘 calculator.
What 수직 항력 Means
Normal 힘 is the support 힘 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 힘 — it is whatever contact 힘 is needed so the object does not sink into the surface.
The most common home일 trap is writing N = mg on every problem. That is true only on a horizontal surface with no other vertical 힘s. Tilts, pushes, lifts, and elevators all change N.
If you already have 질량, angle, and g and only need a 확인ed number, open the free normal 힘 calculator first, then return here for the flat-vs-ramp distinction and 일ed examples.
The 공식s 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.
단위 That Keep Marks Safe
풀이 예제
예제 1: 5.0 kg on a flat floor
g = 9.8 m/s², no extra 힘. N = (5.0)(9.8) = 49 N upward. The floor pushes up 49 N; the block pushes down on the floor with 49 N.
예제 2: same 질량 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.
예제 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.
수직 항력 vs 무게 vs 마찰
무게 mg always points toward Earth’s centre. Normal 힘 is set by the surface direction. 마찰 is usually along the surface and sized from N: Ff = μN. Get N wrong and friction follows it.
For ramp 가속도 and μ_min = tanθ, see how to solve inclined plane problems.
흔한 실수
Sanity 확인: on a ramp, N should be smaller than mg, not larger, unless something extra pushes into the surface.
확인 With the 무료 계산기
Normal 힘 calculator — flat floor, ramp, or extra vertical 힘.
Inclined plane calculator — a, F∥, N, and μ_min together.
마찰 calculator — Ff = μN.
무게 calculator — W = mg before you resolve components.
학습 N = mg versus N = mg cosθ, then confirm every answer on the calculator.