Pulley systems — mechanical advantage — Hinglish notes

1.2.12 · Physics › Newton's Laws & Dynamics

Mechanical Advantage KYA hota hai?

MA KYUN aata hai? (First principles se derive karo)

Key insight: ek ideal (massless, frictionless) rope mein SAME tension hoti hai har jagah.

Ab load ko support karne wale rope segments gino.

Socho ek load ek movable pulley se latka hua hai, jisme $n$ rope segments upar ja rahe hain. Har segment same tension $T$ se upar kheenchta hai. Load (weight $W$ ) equilibrium mein hai:

$\sum F_{up} = \sum F_{down} \Rightarrow n T = W$

Tum un segments mein se ek pakde hue ho, isliye tumhara effort hai $F_{effort} = T$ . Isliye:

$F_{effort} = \frac{W}{n} \Rightarrow IMA = \frac{W}{T} = n$

Distance ka trade-off (energy bookkeeping)

Agar load height $h$ upar uthta hai, to har supporting segment $h$ chhota ho jaata hai. Woh slack tumhare haath se kheencha jaata hai, isliye tum itni length kheenchte ho:

$d_{effort} = n h$

Energy check karo: $W_{in} = F_{effort} d_{effort} = \frac{W}{n} \cdot nh = W h = W_{out} ✓$

Figure — Pulley systems — mechanical advantage

Koi bhi pulley problem KAISE solve karein (method)

Ek rope → ek tension. Har independent rope ko apna $T$ label karo.
Inextensible string ki constraint: rope ki total length constant hai. Do baar differentiate karo ⇒ accelerations ke beech relation milega.
Har mass ka free-body diagram banao, motion ke along $F_{n e t} = ma$ likho.
System solve karo. Static system ke "MA" ke liye $a = 0$ rakho.

Worked Examples

Common Mistakes (Steel-manned)

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho ek heavy bag ko ek hook ke upar se rope daal ke uthana. Mushkil hai. Ab ek moving hook use karo jo bag se attached hai, rope upar, around, neeche jaati hai. Ab do rope-strings bag ko pakde hain, isliye har ek sirf aadha weight uthata hai — kheenchna aadha mushkil lagta hai! Lekin ek pakad hai: bag ko 1 step uthane ke liye, tumhe dono strings se rope reel in karni padti hai, isliye tum do guni rope kheenchte ho. Tumhe strength free mein nahi milti — tum zyada door kheenchne ke liye aasaan kheenchna trade karte ho. 4× aasaan chahiye? 4 strings se bag pakdao.

Flashcards

Mechanical advantage definition

MA = F_{l o a d} / F_{e f f or t}

, woh factor jisse machine tumhara input force multiply karti hai.

Ideal MA of a pulley system equals

movable block ko support karne wale rope strands ki sankhya,

n

Ideal rope mein tension uniform kyun hoti hai?

Massless rope ⇒

F_{n e t} = ma = 0

, aur frictionless pulley sirf direction badalta hai, magnitude nahi.

n

supporting strands ke liye effort par force

F_{e f f or t} = W / n

(kyunki

n T = W

Load ko

h

uthane ke liye kitni distance kheenchni padti hai (

n

strands)

d = nh

, isliye

W_{in} = (W / n) (nh) = W h = W_{o u t}

Single fixed pulley ka MA

1 (sirf force redirect karta hai, multiplication nahi).

Single movable pulley ka MA

Ek movable pulley ke liye string constraint

a_{1} + a_{2} = 2 a_{p u l l ey}

(pulley do ends ki average rate se move karta hai).

Atwood machine acceleration

a = (m_{1} - m_{2}) g / (m_{1} + m_{2})

Atwood machine tension

T = 2 m_{1} m_{2} g / (m_{1} + m_{2})

Real pulley ki efficiency

η = A M A / I M A = W_{o u t} / W_{in}

High MA mein zyada door kyun kheenchna padta hai?

Energy conservation: kam force zyada distance par

F d

constant rakhta hai.

Connections

Newton's Second Law — har FBD yahan $F_{n e t} = ma$ use karta hai.
Tension in strings — uniform tension assumption.
Work–Energy Theorem — $W_{in} = W_{o u t}$ bookkeeping.
Constraint relations — fixed rope length ko differentiate karna.
Atwood machine — dynamic two-mass pulley.
Friction — real-world efficiency loss ka source.
Inclined plane mechanical advantage — same force-for-distance trade.