Foundations — Tension in inextensible strings

1.2.9 · D1 · Physics › Newton's Laws & Dynamics › Tension in inextensible strings

Parent note Tension in Inextensible Strings padhne se pehle, tumhe har woh symbol khud se pata hona chahiye jo woh note use karta hai. Neeche, har symbol ko teen cheezein milti hain: plain words → ek picture → is topic ko iske zaroorat kyun hai. Yeh is order mein hain ki har ek apne pehle waale par tikaa hai.

1. Force $F$ — ek push ya pull

Picture. Figure s01 dekho. Block ko ek blue arrow milti hai jo daayein point kar rahi hai — woh arrow hi force hai. Lamba arrow matlab bada push.

Is topic ko iske zaroorat kyun hai. Tension ek tarah ki force hai (ek pulling wali). Agar tum force ko size + direction ke saath ek arrow ke roop mein nahi soch sakte, tum tension ko bilkul bhi picture nahi kar sakte.

2. Mass $m$ aur weight $mg$ — "matter ki matra" aur gravity ki khiich

Picture. Figure s01 mein, hanging block mein ek orange arrow seedha neeche point karta hai, labelled $mg$. Jab tak mass Earth par hang karta hai woh arrow kabhi nahi badlta.

Is topic ko iske zaroorat kyun hai. Har pulley problem ek mass ke gravity se neeche khinche jaane ($mg$) aur string se upar ruke rehne se shuru hoti hai. Net effect nikalane ke liye tum in do arrows ko subtract karte ho.

3. Acceleration $a$ — speed kitni tezi se badal rahi hai

Picture. Figure s02 mein, ek green arrow woh direction dikhata hai jis taraf object speed up karta hai. Yeh velocity se alag hai — ek object upar move kar sakta hai jabki neeche accelerate kar raha ho (slow ho raha ho).

Is topic ko iske zaroorat kyun hai. Pulley problem ka poora result ek number hai: acceleration $a$. Aur "inextensible" trick do masses ke accelerations ke size mein equal hone ke baare mein ek statement hai.

4. Newton's Second Law $F=ma$ — force acceleration create karti hai

Ise ek sentence ke roop mein padhna. "Object par har arrow add karo. Jo bhi bacha ($F_{\text{net}}$) woh ise accelerate karta hai; zyada bhaari mass usi push ke liye kam accelerate karta hai."

Is topic ko iske zaroorat kyun hai. Parent note mein har tension equation — jaise $m_{1}g-T=m_{1}a$ — bas yahi law ek body ke liye likha hua hai. Poori treatment ke liye Newton's Second Law dekho.

5. Free Body Diagram — SIRF EK object par arrows draw karna

Picture. Figure s03 mein ek hanging block isolated dikhta hai: ek orange arrow $mg$ neeche, ek blue arrow $T$ upar. Jaahan tak us block ka sawaal hai, yahi poori universe hai.

Is topic ko iske zaroorat kyun hai. Tum $F=ma$ apply nahi kar sakte jab tak pata na ho ki kaun si forces add karni hain. FBD woh bookkeeping tool hai jo unhe list karta hai. Free Body Diagrams dekho.

6. Tension $T$ — string ki pulling force

Picture. Figure s03 mein blue $T$ arrow upar point karta hai, block se door, string ke along pulley ki taraf.

Is topic ko iske zaroorat kyun hai. Tension hi poora topic hai. Yahaan har doosra symbol isliye hai taaki tum $T$ involving equations likh aur solve kar sako.

7. Normal force $N$ — surface ki push

Is topic ko iske zaroorat kyun hai. "Block on a table" worked example mein, vertical arrows ($N$ upar, $mg$ neeche) cancel ho jaate hain isliye sirf tension horizontally act karti hai. Vertical direction ko ignore karne ko justify karne ke liye tumhe $N$ chahiye. Normal Force dekho.

8. Inextensible constraint — length kabhi nahi badlti

Is topic ko iske zaroorat kyun hai. Yahi glue hai. Yeh tumhe do unknowns ki jagah dono masses ke liye ek symbol $a$ likhne deta hai. Yeh Constraint Relations ka beej hai.

9. Symbols $\dot{x}$ aur $\ddot{x}$ — "rate of change" dots

Parent ki equation padhna. "${\dot{x}}_1+{\dot{x}}_2=0$" bas yeh kehta hai: do ends ki speeds equal aur opposite hain. Ek aur dot add karo to ${\ddot{x}}_1=-{\ddot{x}}_2$ milta hai: accelerations size mein equal, direction mein opposite hain. Yahi symbol form mein inextensibility ka fact hai.

Prerequisite map

Ise upar se neeche padho: forces + mass + acceleration Newton's law banate hain; woh plus FBD tumhe har body ke liye tension equation likhne deta hai; inextensible constraint dono bodies ko ek shared $a$ se jodta hai; milke yeh hi topic hai.

Equipment checklist

Daayein taraf cover karo aur khud ko test karo. Agar koi bhi answer fuzzy lage, parent note se pehle woh section dobara padho.

Connections

• Newton's Second Law — har tension equation ke peeche ka law.
• Free Body Diagrams — woh tool jo add karne ke liye arrows list karta hai.
• Normal Force — surface ki perpendicular push, tension ki cousin.
• Constraint Relations — "inextensible ⟹ same $a$" ki general form.
• Atwood Machine — pehli jagah jahan yeh saare symbols combine hote hain.
• Frictionless Pulleys vs Pulleys with Inertia — jahan uniform tension break ho sakta hai.
• Tension in Inextensible Strings — woh parent topic jiske liye yeh page tumhe prepare karta hai.