Foundations — Non-conservative forces — friction, air drag

1.3.7 · D1 · Physics › Work, Energy & Power › Non-conservative forces — friction, air drag

Pehle tum parent note padh sako, uske liye tumhare paas uska alphabet hona zaroori hai. Hum har piece ko zero se build karte hain, ek aisi order mein jahan har symbol earn kiya jaata hai use use karne se pehle.

0. Teen "given" numbers — $m$, $g$, $h$

Yeh dono is page ke almost har formula mein aate hain, isliye hum inhe pehle define karte hain, kuch bhi build hone se pehle.

1. Woh arrow jo direction carry karta hai — ek vector

Figure s01 dekho. Lal arrow ek velocity vector $\vec{v}$ hai: block upar-daayein move kar raha hai. Uski length speed batati hai; uska tilt direction batata hai.

Figure s01 — ek velocity vector: length speed encode karta hai, tilt direction encode karta hai.

• $\vec{r}$ = position vector: origin se object ki abhi ki jagah tak ka arrow.
• $d\vec{r}$ = object ke path ke saath ek chhota sa step — itna chhota arrow ki almost ek dot lagta hai, us direction ki taraf pointing karta hai jis taraf object us instant mein move kar raha hai.

2. Chhoti topi — ek unit vector $\hat{v}$

Toh $\vec{v}=v\hat{v}$ padha jaata hai: "velocity = (kitni tezi se) times (kis taraf)." Number $v$ (koi arrow nahi, koi hat nahi) plain speed hai.

3. Do arrows ko multiply karna — dot product $\vec{F}\cdot d\vec{r}$

Yeh is page ka sabse important tool hai. Jab ek force $\vec{F}$ act karta hai jabki object ek step $d\vec{r}$ leta hai, toh woh force actually motion mein kitni help kar rahi hai?

Figure s02 — teen panels: force motion step ke saath aligned ($0^{\circ }$), sideways ($90^{\circ }$), aur opposed ($180^{\circ }$).

Teen cases jo tumhe kabhi nahi bhoole chahiye (Figure s02 ke teen panels, left se right):

• Same direction ($\varphi =0$): $\cos 0=1$ → poora positive contribution. Force help karta hai.
• Right angle ($\varphi =90^{\circ }$): $\cos 90^{\circ }=0$ → zero. Sideways force kuch nahi karta.
• Opposite direction ($\varphi =180^{\circ }$): $\cos 180^{\circ }=-1$ → poora negative. Force motion se ladhta hai.

4. Saare chhote steps ko add karna — integral $\int$ aur loop $\oint$

Ise ek total ki tarah socho. Har step thoda sa work contribute karta hai; integral poora dhera hota hai.

Figure s03 — ek closed loop: start equals end, phir bhi friction (lal arrows) har leg ko oppose karta hai.

• $L$ = total path length: travel ki gayi poori distance, puri squiggly line ki length — straight-line displacement nahi.
• displacement = start se finish tak ka single straight arrow. Ek closed loop par displacement zero hota hai, lekin $L$ bada hota hai. Yeh gap is poore topic ka dhadakta dil hai.

5. Energy ke words — $KE$, $U$, $E_{mech}$, $W$, $W_{nc}$, $Q$

Triangle $\Delta$ (Greek "delta") ka matlab hai "change in": $\Delta KE=K{E}_{\text{final}}-K{E}_{\text{initial}}$.

6. Friction cast — $N$, ${\mu }_k$, $f_k$, $\theta$

Figure s04 — incline par ek block: weight $mg$ (seedha neeche) do parts mein split — ek surface mein press karta hai ($mg\cos \theta$) aur ek surface ke saath slide karta hai ($mg\sin \theta$).

7. Drag ka cast — $v$, $b$, $C_d$, $\rho$, $A$, $v_t$ — aur actual drag formula

Prerequisite map

Upar har foundation topic box mein flow karta hai. Agar koi bhi incoming arrow tumhe unclear lagta hai, parent note kholne se pehle us section ko dobara dekho.

Equipment checklist

Daayein side cover karo aur khud ko test karo. Agar tum sab ka jawab de sako, tum ready ho.

Connections

• Parent topic — Non-conservative forces (Hinglish) — woh note jiske liye yeh page tumhe taiyaar karta hai.
• Conservative forces & potential energy — jahan $U$ properly build hoti hai.
• Work–Energy theorem — jahan $W=\Delta KE$ aata hai.
• Friction — static & kinetic — ${\mu }_k$ aur $N$ par deeper.
• Terminal velocity & projectile with drag — yahan ke har drag symbol ko use karta hai.