Normal force — reaction force, not always = mg

1.2.5 · Physics › Newton's Laws & Dynamics

Normal Force KIYA hai?

Yeh exist kyun karta hai? Solid surfaces atoms se bane hote hain jo electromagnetic bonds se jude hote hain. Jab aap kisi object ko surface par dabaate ho, surface microscopically deform hoti hai (ek stiff spring ki tarah), aur bonds push back karte hain. Jitna zyada push karo, utna zyada push back karta hai — isliye $N$ apne aap ko situation ke hisaab se adjust karta hai.

"Hamesha $m g$ nahi" kyun? Kyunki $N$ ko surface ke normal direction mein Newton's second law apply karke find kiya jaata hai, kisi formula se nahi. Jo bhi cheez net normal-direction requirement ko badlegi, woh $N$ ko bhi badlegi.

$N$ kaise find karein — universal method

Derivation: flat-ground case (jahan $N = m g$ sach mein hold karta hai)

Mass $m$ ka object ek horizontal floor par rakhaa hai. Forces: gravity $m g$ neeche, normal $N$ upar. Koi vertical acceleration nahi ( $a = 0$ ). $\sum F_{y} = N - m g = m a_{y} = 0 \Rightarrow == N = m g ==$

Yeh step kyun? Hum $a_{y} = 0$ isliye set karte hain kyunki object vertically accelerate nahi kar raha. Sirf inhi assumptions ke under $N = m g$ hota hai.

Figure — Normal force — reaction force, not always = mg

Cases jahan $N \neq = m g$ hota hai

1. Extra vertical push ya pull

Floor par rakhe block ko force $F$ se neeche push karo: $\sum F_{y} = N - m g - F = 0 \Rightarrow N = m g + F$ $F$ se upar pull karo: $N = m g - F$ Kyun? $N$ woh baaki baccha hua value supply karta hai taaki $a_{y} = 0$ rahe.

2. Elevator / vertical acceleration

Mass $m$ ka person ek elevator mein hai jo upar $a$ acceleration se ja raha hai: $\sum F_{y} = N - m g = ma \Rightarrow == N = m (g + a) ==$ Neeche $a$ se accelerate karna: $N = m (g - a)$ . Free fall ( $a = g$ ): $N = 0$ (weightlessness!). Kyun? Jo "weight tumhe feel hota hai" woh actually $N$ hai, floor ka push — gravity nahi.

3. Inclined plane

Angle $θ$ ke frictionless incline par block. Gravity ko surface ke $⊥$ aur $∥$ components mein resolve karo. Normal direction mein koi acceleration nahi hota (block slope ke saath slide karta hai, usme nahi): $\sum F_{⊥} = N - m g cos θ = 0 \Rightarrow == N = m g cos θ ==$ $cos θ$ kyun? Sirf gravity ka woh component jo surface ke perpendicular hai, use $N$ se balance karna hota hai. Kyunki $θ < 9 0^{\circ}$ , $cos θ < 1$ , isliye $N < m g$ .

4. Accelerate ho raha inclined plane (steel-man trap)

Agar incline khud horizontally accelerate kare, toh $a_{⊥} \neq = 0$ aur $N$ phir se badal jaata hai — hamesha $\sum F_{⊥} = m a_{⊥}$ par wapas jaao.

Recall Feynman: ek 12-saal ke bachche ko samjhao

Soch trampoline par khade ho. Trampoline tumhare pairon ko upar push karta hai taaki tum gir na jao — woh push hi normal force hai. Agar koi dost tumhare kaandhon par neeche dhakaaye, trampoline zyada push back karta hai tum dono ko hold karne ke liye. Agar trampoline ka floor suddenly gira diya jaaye (free fall), toh woh push karna band kar deta hai aur tum weightless feel karte ho. Aur ek slide (slope) par, floor sirf slide se seedha bahar push karta hai, seedha upar nahi — isliye use tumhare poore weight jaisa zyada push nahi karna padta. Push kabhi bhi fixed number nahi hota; yeh hamesha exactly itna hota hai ki tum andar na dhans sako.

Active Recall

Normal force kya hota hai?

Woh perpendicular contact force jo surface kisi object par lagati hai, use surface se door push karti hai; ek constraint/reaction force jiska value interpenetration rokne ke liye adjust hota hai.

Kya normal force hamesha mg ke barabar hoti hai?

Nahi — sirf horizontal surface par jab koi extra vertical force na ho aur koi vertical acceleration na ho. Warna

\sum F_{⊥} = m a_{⊥}

solve karo.

N find karne ka general method kya hai?

Newton's 2nd law ko surface-normal direction mein apply karo:

\sum F_{⊥} = m a_{⊥}

, phir N ke liye solve karo.

Angle θ ke frictionless incline par block ke liye N?

N = m g cos θ

, kyunki sirf gravity ka perpendicular component balance karna hota hai.

Upar acceleration a se jaate elevator mein mass m ke liye N?

N = m (g + a)

Free fall mein N?

N = 0

— weightlessness; surface ko ab push karne ki zaroorat nahi.

Floor par rakhe block ko extra force F se neeche push karo — N kya hoga?

N = m g + F

Kya N (floor on box) aur mg (Earth on box) Newton's-3rd-law pair hain?

Nahi — yeh dono same body par act karte hain. N ka reaction box ka floor ko neeche push karna hai.

N physically kyun exist karta hai?

Surface ke microscopically compress hone par atoms ke beech electromagnetic repulsion, ek stiff spring ki tarah push back karta hai.

Connections

Newton's Second Law — woh engine jo $N$ determine karta hai
Newton's Third Law — clarify karta hai ki $N$ ka asli reaction kya hai
Friction — kinetic/static friction, $N$ ke proportional hota hai ( $f = μ N$ )
Inclined Plane Problems — jahan $N = m g cos θ$
Apparent Weight & Elevators — $N = m (g \pm a)$
Free Body Diagrams — woh tool jo $\sum F_{⊥}$ setup karne ke liye use hota hai