WHY does it exist? Solid surfaces are made of atoms held by electromagnetic bonds. When you press an object onto a surface, the surface deforms microscopically (like a stiff spring), and the bonds push back. The harder you push, the harder it pushes — so Nadjusts itself to the situation.
WHY "not always mg"? Because N is found by applying Newton's second law in the direction normal to the surface, not by a formula. Anything that changes the net normal-direction requirement changes N.
Person of mass m in an elevator accelerating up with a:
∑Fy=N−mg=ma⇒==N=m(g+a)==
Accelerating down with a: N=m(g−a). Free fall (a=g): N=0 (weightlessness!).
Why? The "weight you feel" is actually N, the floor's push — not gravity.
Block on a frictionless incline at angle θ. Resolve gravity into components ⊥ and ∥ to surface. Along the normal there's no acceleration (block slides along the slope, not into it):
∑F⊥=N−mgcosθ=0⇒==N=mgcosθ==Why cosθ? Only the component of gravity perpendicular to the surface must be balanced by N. Since θ<90∘, cosθ<1, so N<mg.
If the incline itself accelerates horizontally, a⊥=0 and N changes again — always go back to ∑F⊥=ma⊥.
Recall Feynman: explain to a 12-year-old
Imagine standing on a trampoline. The trampoline pushes up on your feet so you don't fall through — that push is the normal force. If a friend pushes down on your shoulders, the trampoline pushes back harder to hold both of you. If the trampoline floor were suddenly dropped (free fall), it stops pushing and you feel weightless. And on a slide (a slope), the floor only pushes straight out of the slide, not straight up — so it doesn't have to push as hard as your full weight. The push is never a fixed number; it's always exactly enough to keep you from sinking in.
The perpendicular contact force a surface exerts on an object, pushing it away from the surface; a constraint/reaction force whose value adjusts to prevent interpenetration.
Is normal force always equal to mg?
No — only on a horizontal surface with no extra vertical forces and no vertical acceleration. Otherwise solve ∑F⊥=ma⊥.
General method to find N?
Apply Newton's 2nd law along the surface-normal direction: ∑F⊥=ma⊥, then solve for N.
N for a block on a frictionless incline of angle θ?
N=mgcosθ, because only the perpendicular component of gravity must be balanced.
N for mass m in an elevator with upward acceleration a?
N=m(g+a).
N in free fall?
N=0 — weightlessness; the surface no longer needs to push.
Push down with extra force F on a block on the floor — what is N?
N=mg+F.
Are N (floor on box) and mg (Earth on box) a Newton's-3rd-law pair?
No — they act on the same body. The reaction to N is the box pushing down on the floor.
Why does N exist physically?
Electromagnetic repulsion between atoms as the surface microscopically compresses, like a stiff spring pushing back.
Dekho, normal force ka matlab hai woh push jo koi surface aapke object par deti hai, hamesha surface ke perpendicular (90 degree) direction me. Ye ek reaction force hai — matlab surface utni hi zor se push karti hai jitni zaroorat hoti hai object ko andar ghusne se rokne ke liye. Isiliye iska value fix nahi hota. Bahut log soch lete hain ki "N hamesha mg ke barabar hoti hai" — galat! Ye sirf tab true hai jab object flat zameen par ho, koi extra vertical force na ho, aur vertical acceleration zero ho.
N nikalne ka asli tarika ek hi hai: surface ke perpendicular direction me Newton's second law lagao — ∑F⊥=ma⊥ — aur N solve kar lo. Jaise lift me agar upar acceleration a hai, to N=m(g+a), isiliye aapko bhaari mehsoos hota hai. Niche jaate waqt N=m(g−a), halka lagta hai. Aur free fall me N=0 — bilkul weightless! Incline (dhalan) par sirf gravity ka perpendicular component balance karna padta hai, isiliye N=mgcosθ, jo mg se kam hota hai.
Ek important point: N aur gravity (mg) Newton ke third law ke action-reaction pair NAHI hain, kyunki dono ek hi body par lag rahe hain. Real reaction to N ka ye hai ki box neeche floor par push karta hai. Isko yaad rakho exam me — ye trap bahut aata hai. Toh hamesha free body diagram banao, perpendicular axis choose karo, aur N ko situation se nikalo — ratto mat.
