Free body diagrams — systematic drawing technique

1.2.4 · Physics › Newton's Laws & Dynamics

Free Body Diagram KYA hota hai?

Teen words jo matter karte hain:

Free — body apne surroundings se free (isolate) ki gayi hai.
Body — ek chosen object (woh "system").
Diagram — pure force picture, aur kuch nahi.

KAISE: systematic recipe (80/20 core)

Figure — Free body diagrams — systematic drawing technique

Diagram se equations DERIVE karna

FBD algebra ka bridge hai. Jab arrows draw ho jaate hain, Newton ka 2nd law har axis ke liye alag ho jaata hai:

$\sum F_{x} = m a_{x} \sum F_{y} = m a_{y}$

Worked Example 1 — Table par block, aap horizontally push karte ho

Ek block (mass $m$ ) ek rough table par rakha hai. Aap horizontally force $F$ se push karte ho. FBD draw karo aur acceleration nikalo.

Step 1–2: System = block, dot mein shrink karo. Yeh step kyun? Yeh fix karta hai ki "external" ka matlab kya hai — table aur aapka haath environment hain.

Step 3: Gravity $m g$ neeche. Kyun? Long-range, hamesha wahan hoti hai.

Step 4 (contacts): Block table ko touch karta hai (→ normal $N$ upar, friction $f$ peeche motion ko oppose karta hua) aur aapka haath (→ applied $F$ aage). Friction peeche kyun? Friction slide karne ki tendency ko oppose karta hai; block aage slide karna chahta hai, toh $f$ peeche point karta hai.

Step 6 — resolve: $y : N - m g = 0 \Rightarrow N = m g$ = 0 kyun? Koi vertical acceleration nahi (block table par hi rehta hai). $x : F - f = ma \Rightarrow a = \frac{F - f}{m}$ Kyun? Net horizontal force horizontal acceleration drive karta hai.

Worked Example 2 — Frictionless incline par block (angle $θ$ )

Steps 1–4: System = block. Gravity $m g$ neeche. Surface contact → normal $N$ ⊥ incline ke. Koi friction nahi.

Step 6 — axes tilt karo taaki $x$ down-slope point kare, $y$ ⊥ slope. Tilt kyun? Taaki acceleration purely $x$ ke along ho; $a_{y} = 0$ .

Gravity resolve karo (sirf tilted force):

Incline ke along component (down-slope): $m g sin θ$
Perpendicular component (surface mein): $m g cos θ$

Along-slope ke liye $sin$ kyun? Jab $θ \to 90°$ (vertical wall) tab slope direction vertical ho jaati hai, aur gravity poori tarah us par act karti hai — $sin 90° = 1$ . ✓ Yeh sanity check batata hai ki trig function kahan jaata hai.

$y : N - m g cos θ = 0 \Rightarrow N = m g cos θ$ $x : m g sin θ = ma \Rightarrow a = g sin θ$

$a$ mein $m$ kyun nahi? Mass cancel ho jaata hai — heavier blocks faster nahi hote, bilkul free-fall ki tarah.

Worked Example 3 — String aur pulley se jude do blocks (Atwood-ish, table par)

Block $A$ ( $m_{1}$ ) frictionless table par, string ek pulley ke upar se hanging block $B$ ( $m_{2}$ ) tak.

Do FBDs — ek per body! Do kyun? Har body ko apna diagram chahiye; tension unhe link karta hai.

FBD of $A$ (horizontal): tension $T$ aage, $N$ upar, $m_{1} g$ neeche. $T = m_{1} a$ FBD of $B$ (hanging): weight $m_{2} g$ neeche, tension $T$ upar. $m_{2} g - T = m_{2} a$ Same $T$ , same $a$ kyun? Ek ideal string (massless, inextensible) → poori length mein equal tension aur equal speed.

Dono equations add karo ( $T$ eliminate karo): $m_{2} g = (m_{1} + m_{2}) a \Rightarrow a = \frac{m _{2}}{m _{1} + m _{2}} g$ Add kyun? Yeh internal tension cancel kar deta hai, sirf driving weight vs total inertia bachti hai.

Common Mistakes (Steel-manned)

Recall Feynman: ek 12-saal-ke bachche ko samjhao

Socho tum ek detective ho aur object ek suspect hai. Tum suspect ke liye ek dot draw karte ho aur phir har us cheez ke liye ek arrow draw karte ho jo use touch kar rahi hai ya pull kar rahi hai — floor upar push kar raha hai, gravity neeche pull kar rahi hai, ek rope side mein tug kar raha hai. Tum suspect ka doosron par push nahi draw karte (woh alag suspect ka diagram hai), aur tum "woh kitni tez daud raha hai" nahi draw karte — sirf pushes. Jab saare push-arrows draw ho jaayein, tum unhe sirf do directions mein scores ki tarah add karo, aur woh batata hai ki suspect kis direction mein aur kitni tezi se speed up karta hai.

Active Recall

Free body diagram kya hota hai?

Ek single isolated body ka diagram jo us par act karne waali saari external forces ko ek point se arrows ke roop mein dikhata hai, labels ke saath — aur kuch nahi.

FBD recipe mein, pehle kaun si force draw karte hain aur kyun?

Gravity (

m g

neeche) — yeh ek long-range force hai jo hamesha present hoti hai, isliye kabhi bhool nahi sakte.

Contact forces count karne ka rule kya hai?

Body ko touch karne waali har surface/string ke liye ek set of contact forces; koi touch nahi ⇒ wahan koi contact force nahi.

ma

FBD par arrow ke roop mein kyun nahi aana chahiye?

Yeh net force ka result hai (

\sum F = ma

ka right side), koi physical push ya pull nahi.

Angle

θ

ke slope par normal force kya hoti hai?

N = m g cos θ

(gravity ka component surface ke perpendicular).

Frictionless incline par block ka acceleration kya hoga?

a = g sin θ

(mass cancel ho jaata hai).

Incline par coordinate axes tilt kyun karte hain?

Taaki acceleration ek axis ke along ho aur doosre ke along zero, ek unknown hata ke.

Jab tum block ko aage push karte ho toh friction peeche kyun point karta hai?

Friction relative-slip tendency ko oppose karta hai; aage push karne se woh aage slide karna chahta hai, isliye friction peeche act karta hai.

Two-block string-pulley system mein tension aur acceleration dono ke liye same kyun hote hain?

Ek ideal (massless, inextensible) string equal tension transmit karti hai aur equal speeds force karti hai.

Reaction force same FBD par action ke saath kyun nahi draw kar sakte?

Action–reaction pairs alag bodies par act karte hain; ek FBD sirf ek body par forces dikhata hai.

Connections

Newton's Second Law — FBD seedha $\sum F = m a$ mein jaata hai.
Newton's Third Law — explain karta hai ki reaction forces doosri bodies ke diagrams par kyun hoti hain.
Normal Force and Friction — contact forces jo aap sabse zyada draw karoge.
Tension in Strings and Pulleys — multi-body FBD coupling.
Inclined Plane Problems — axis-tilting ka canonical application.
Resolving Vectors into Components — arrows draw karne ke baad ka math step.