Chapter 03: Machines - Vardaan Class Revision Notes

I. PRINCIPLES & FORMULAS

M.A.$M.A. = \frac{Load (L)}{Effort (E)}$

V.R.$V.R. = \frac{d_E}{d_L}$

Efficiency$\eta \% = \frac{M.A.}{V.R.} \times 100$

Relationship$M.A. = V.R. \times \eta$

Note 1: M.A. decreases due to friction/weight. V.R. is constant (geometric property).

Note 2: Ratio of similar quantities $\to$ No Units for M.A., V.R., or $\eta$.

II. LEVERS (LAW: $L \times L_{arm} = E \times E_{arm}$)

Class	Logic (Middle)	M.A. Constraint	Typical Examples
Class I	Fulcrum (F)	$>1, =1, <1$	Crowbar ($>1$), Seesaw ($=1$), Scissor ($<1$)
Class II	Load (L)	Always > 1	Nutcracker, Wheelbarrow, Paper Cutter
Class III	Effort (E)	Always < 1	Fire Tongs, Bread Knife, Human Forearm

[IMAGE: Lever Classes Summary Diagram]

Clean comparison of F-L-E positions with directional arrows for All Classes.

Human Body Levers:

Class I: Nodding head (Fulcrum: spinal joint, Load: head weight, Effort: neck muscle).
Class II: Raising on toes (Fulcrum: toes, Load: body weight, Effort: ankle muscle).
Class III: Foreground lift (Fulcrum: elbow, Effort: biceps attachment, Load: weight in hand).

III. PULLEY MASTER TABLE

System Type	Ideal M.A.	V.R.	Practical Change
Single Fixed	1	1	MA < 1 (Friction)
Single Movable	2	2	MA < 2 (Weight/Friction)
Block & Tackle	$n$	$n$	$\eta = 1 - \frac{w}{nE}$

Master Strategy: The $2^n$ System For **one fixed pulley** and **$n$ movable pulleys**, the $V.R. = 2^n$.
Ex: 3 movable pulleys $\to V.R. = 2^3 = 8$.

IV. TOP REVISION NUMERICALS

#1 Lever calculation Q: Crowbar of $1.5\text{ m}$. Fulcrum at $0.5\text{ m}$ from load. Find M.A.
Ans: $L_{arm} = 0.5, E_{arm} = 1.5 - 0.5 = 1.0$. $M.A. = 1/0.5 = \mathbf{2}$.

#2 Nutcracker Force Q: Handle $20\text{ cm}$, Nut at $2\text{ cm}$ from hinge. Load needed $= 40\text{ kgf}$. Find Effort.
Ans: $E \times 20 = 40 \times 2 \implies \mathbf{E = 4\text{ kgf}}$.

#3 Block & Tackle (n=5) Q: Load $= 4500\text{ N}$, Effort $= 1000\text{ N}$, Pulleys $= 5$. Find $\eta$.
Ans: $V.R. = 5, M.A. = 4500/1000 = 4.5. \eta = 4.5/5 = \mathbf{90\%}$.

#4 Power Input Q: Fixed pulley lifts $750\text{ N}$ using $1000\text{ N}$ mass falling $8\text{ m}$ in $4\text{ s}$. Find Power Input.
Ans: Work In $= 1000 \times 8 = 8000\text{ J}$. Power $= 8000/4 = \mathbf{2000\text{ W}}$.

Quick Check: M.A. Trends - If $\eta < 100\%$, then **M.A. < V.R.** - If weight of movable block increases, **M.A. decreases**. - To increase Efficiency, **decrease weight of movable block**.

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