Atwood machine — derivation: Foundations — Hinglish deep dive

1.2.10 · D1 · Physics › Newton's Laws & Dynamics › Atwood machine — derivation

Derivation padhne se pehle, tumhe uske har symbol ko apna banana hoga. Yeh page har ek symbol ko ek picture se build karta hai, usi order mein jis order mein wo ek doosre pe depend karte hain. Yahan kuch bhi yeh assume nahi karta ki tumne parent derivation dekhi hai.

0. Woh scene jo hum describe kar rahe hain

Pehle physical picture fix karte hain taaki baad ke har symbol ka ek ghar ho. Neeche ke figure mein, labels dekho: wheel ko pulley kaha jaata hai, cord ko string, aur dono ends se do blocks latke hain. Chhote arrows motion ke directions dikhate hain jab left block bhaari hota hai. (Blocks ko unke symbols $m_{1}$ aur $m_{2}$ Section 1 mein milenge, jab hum "mass" define karenge.)

Neeche sab kuch usi ek picture ki chezon ka careful naam rakhna hai.

1. Mass — symbol $m$

2. Gravity ki pull — $g$ aur weight $m g$

Blocks move kyun karte hain? Kyunki Earth unhe neeche kheenchti hai. Hume "kitni strongly" ka ek number chahiye.

3. Speed, velocity, aur acceleration — symbol $a$

"Positive directions" ki baat karne se pehle, hume wo quantity chahiye jiska direction hota hai aur jise hum ultimately solve karte hain. Yeh ek pehle wale shabd se banti hai: velocity.

4. Force aur arrow picture

Kyunki forces ka direction hota hai, unhe add karne se pehle hume decide karna hoga ki kaunsa direction positive hai. Yahi woh jagah hai jahan zyattar beginners slip karte hain — isliye ise bhi ek picture banate hain.

5. Tension — symbol $T$

String kheenchti hai. Us pull ka apna naam hai.

6. Dono magic string-properties

Definition mein do idealised words bahut bada kaam karte hain. Inhe earn karte hain.

7. Newton's Second Law aur free body diagram

Upar sab kuch ek single law mein pour hota hai.

Ise apply karne ke liye hum ek free body diagram draw karte hain: ek block ko isolate karo, sirf woh arrows draw karo jo use touch kar rahe hain (gravity neeche, tension upar), phir unhe $F_{n e t}$ mein add karo. Neeche ka figure exactly yahi dikhata hai dono blocks ke liye.

Recall Free body diagram, ek line mein

Question: har latke block pe kaun si do forces kaam karti hain? ::: gravity $m g$ neeche aur tension $T$ upar — aur kuch nahi. Dekho Free Body Diagrams.

8. Dono edge cases — equal masses, aur bhaari block kisi bhi side pe

9. Harmonic-mean shape (ek preview)

Tension ka answer $\frac{2 m _{1} m _{2}}{m _{1} + m _{2}} g$ jaisa niklegaa. Tumhe yahan derive karne ki zarurat nahi — bas shape pehchaano, aur $g$ notice karo: tension ek force hai (newtons), isliye isme $g$ hona chahiye, exactly jaise weight mein hota hai.

Yeh foundations topic ko kaise feed karte hain

Is map ko top-to-bottom padho: upar ke plain-language boxes building blocks hain; arrows dikhate hain kaunsa idea agle mein feed hota hai; sab kuch neeche Atwood derivation mein funnel hota hai.

Equipment checklist

Right side cover karo aur khud test karo. Agar koi bhi jawaab surprising lage, to derivation se pehle woh section dobara padho.

m

kya measure karta hai, aur kis unit mein?

Stuff ki matra (inertia), kilograms mein.

g

saral shabdon mein kya hai?

Gravity har second kitni downward speed (m/s) add karti hai;

\approx 9.8 m/s^{2}

Mass

m

ke block ka weight likho.

m g

(ek force, newtons mein, neeche point karta hua).

Speed aur velocity mein kya fark hai?

Speed = kitna fast; velocity = kitna fast plus direction.

Symbol

a

kise represent karta hai?

Acceleration — velocity kitni tezi se change hoti hai,

m/s^{2}

mein.

F_{n e t}

ka matlab kya hai?

Ek body pe saare force arrows (signs ke saath) add karne ke baad bachi hui single leftover force.

String (rope) kya kar sakti hai — push, pull, ya dono?

Sirf pull; tension block se pulley ki taraf point karti hai.

Kya "string" aur "rope" yahan alag cheezein hain?

Nahi — dono ek hi idealised inextensible, massless cord hain.

Rope mein tension

T

poori rope mein same kyun hai?

String massless hai, isliye kisi bhi piece pe net force zero hona chahiye.

"Inextensible" dono blocks ke baare mein kya force karta hai?

Unka equal displacement, speed, aur acceleration magnitude hota hai.

Forces add karne se pehle sign convention kyun chahiye?

Forces ka direction hota hai; tumhe fix karna hoga kaunsa way "+" hai unhe sahi se add karne ke liye.

Newton's Second Law batao.

F_{n e t} = ma

Ek hanging block ke liye free body diagram kya dikhata hai?

Sirf gravity

m g

neeche aur tension

T

upar.

Agar

m_{1} = m_{2}

hai, to acceleration kya hai aur kyun?

a = 0

— dono weights balance karte hain, isliye koi net driving force nahi hai.

Agar

m_{2} > m_{1}

hai, to kaunsa block neeche jaata hai?

m_{2}

(bhaari side neeche jaati hai); wahi formulas apply hote hain.

Tension formula

m_{1}

aur

m_{2}

mein symmetric kyun hai?

Dono blocks ko swap karne se rope ki pull nahi badal sakti.

Connections

Atwood machine — derivation (index 1.2.10) — woh page jo yeh foundations unlock karta hai.
Newton's Second Law — woh single equation jisme sab kuch reduce hota hai.
Free Body Diagrams — hum ek block ke arrows kaise isolate karte hain.
Tension in Strings — $T$ ek uniform value kyun hai.
Constraint Relations — inextensible string ⇒ equal accelerations.
Pulley Systems & Mechanical Advantage — pulley rope ke saath kya karta hai.
Harmonic Mean — tension answer ki shape.