Machines – ICSE Class 10 Physics

        Machines chapter is a goldmine in ICSE — easy to understand, lots of direct formula-based questions, and the numericals are very predictable. I'll walk you through everything: levers, pulleys, block and tackle, MA, VR, efficiency — with the kind of breakdown I wish I had when I was preparing.
    

1) What is a Machine?

A machine is a device that makes work easier by:

Multiplying force (so you can lift heavy stuff with less effort)
Changing the direction of force (pulling down to lift up)
Increasing the speed of work

Simple machines you already know — lever, pulley, inclined plane, screw, wedge, wheel and axle. But in ICSE Class 10, we focus on levers and pulleys mainly.

2) Key Terms — Load, Effort, Fulcrum

Term	Symbol	Meaning	Unit
Load	L	The weight or resistance that the machine has to overcome	N, kgf, gf
Effort	E	The force applied on the machine to overcome the load	N, kgf, gf
Fulcrum / Pivot	—	The fixed point about which the machine rotates	—

3) Mechanical Advantage (MA)

MA tells you how many times the machine multiplies the applied effort. It's the ratio of load to effort.

M.A. = Load / Effort = L / E MA has NO unit (it's a ratio — same units cancel out)

Conditions of MA — This Is What ICSE Asks

Condition	What it means	Example
MA > 1	Machine multiplies force. You apply less effort to lift more load.	Nutcracker, crowbar, movable pulley
MA = 1	Machine just changes direction. Effort = Load.	Single fixed pulley
MA < 1	Machine doesn't multiply force — used for speed or range.	Class III lever (tweezers, fishing rod)

4) Velocity Ratio (VR)

VR is the ratio of the distance moved by the effort to the distance moved by the load in the same time.

V.R. = Distance moved by effort / Distance moved by load VR also has NO unit

VR depends only on the design of the machine, not on friction. So VR is always constant for a given machine. This is a key difference from MA — MA can change if there's friction, but VR stays fixed.

5) Efficiency (η)

No machine is perfect — some energy is always wasted overcoming friction. Efficiency tells you how much of the input work is usefully converted into output work.

Formula + Derivation

Work input = Effort × distance moved by effort = E × d_E Work output = Load × distance moved by load = L × d_L Efficiency (η) = Work output / Work input = (L × d_L) / (E × d_E) = (L / E) × (d_L / d_E) = MA × (1 / VR) = MA / VR η = MA / VR In percentage: η% = (MA / VR) × 100%

For an ideal machine (no friction): MA = VR, so η = 1 or 100%. But in real life, η is always less than 100%.

Want to remember this derivation easily? Just think: Output/Input = (L×d_L)/(E×d_E) = L/E × d_L/d_E = MA × 1/VR = MA/VR. Write it once and it'll click. This exact derivation has come in ICSE boards multiple times.

6) Relationship Between MA, VR, and η

MA = VR × η MA < VR for a real machine (since η < 1) MA = VR for an ideal machine (η = 1)

7) Work Output and Work Input

Work input = work done by the effort on the machine.
Work output = useful work done by the machine on the load.

Work input > Work output (always, because of friction)
Wasted work = Work input - Work output
Wasted work is usually used to overcome friction

8) Principle of a Machine

The principle of a machine states that: "In an ideal machine (no friction), the work done by the effort (work input) is equal to the work done by the load (work output)."

For an ideal machine: Work input = Work output E × d_E = L × d_L L / E = d_E / d_L → MA = VR

9) Levers

A lever is a rigid bar that rotates about a fixed point (fulcrum). Levers are classified into three classes based on the relative positions of load, effort, and fulcrum.

Class I Lever — Fulcrum in the Middle

Fulcrum between Load and Effort

MA > 1 if effort arm > load arm (like a crowbar)
MA = 1 if effort arm = load arm (like a see-saw balanced)
MA < 1 if effort arm < load arm
Examples: Crowbar, see-saw, scissors, pliers, pincer

Class II Lever — Load in the Middle

Load between Fulcrum and Effort

Effort arm > Load arm always → MA > 1 always
These levers always multiply force
Examples: Nutcracker, bottle opener, wheelbarrow, punching shears

Class III Lever — Effort in the Middle

Effort between Fulcrum and Load

Effort arm < Load arm always → MA < 1 always
These levers don't multiply force — they increase speed/range of motion
Examples: Tweezers, fishing rod, tongs, human forearm, broom

Class	Arrangement	MA	Examples
I	F—L—E or L—F—E	Can be >1, =1, or <1	Crowbar, see-saw, scissors
II	F—E—L (L in middle)	Always > 1	Nutcracker, wheelbarrow
III	F—L—E (E in middle)	Always < 1	Tweezers, fishing rod

10) Pulley Systems

Single Fixed Pulley

Pulley is fixed to a support. You pull down to lift up.
MA = 1, VR = 1
Does NOT multiply force — just changes direction of effort
Efficiency η < 100% due to friction

Single Movable Pulley

Pulley moves with the load. One end of the string is fixed, effort is applied at the other end.
MA = 2, VR = 2 (ideally)
Effort needed is half the load (in ideal case)
The load is supported by 2 segments of the string

        Remember this trick: VR of a pulley system = Number of rope segments supporting the movable block / load. For a single movable pulley, the load is supported by 2 rope segments, so VR = 2.
    

Block and Tackle System

The block and tackle system uses multiple pulleys arranged in two blocks — one fixed and one movable. The combination multiplies force significantly.

For a block and tackle with n pulleys in each block (or n rope segments): VR = n (number of rope segments supporting the load) MA = n × η (ideally MA = n if η = 100%) Effort E = L / MA = L / (n × η)

How to find VR: Simply count the number of rope segments that support the movable (lower) block. That number is your VR.

System	MA (ideal)	VR	Change direction?
Single fixed pulley	1	1	Yes
Single movable pulley	2	2	No
Block and tackle (2 pulleys each)	4	4	Yes
Block and tackle (n segments)	n	n	Depends on design

11) Solved Numericals

Numerical 1 — Lever (Class I)

A crowbar of length 120 cm has its fulcrum at 20 cm from the load. A load of 60 kgf is to be lifted. Calculate the effort required and MA.

Load arm = distance from fulcrum to load = 20 cm Effort arm = 120 - 20 = 100 cm MA = Effort arm / Load arm = 100 / 20 = 5 MA = L / E → 5 = 60 / E → E = 12 kgf So just 12 kgf lifts 60 kgf. That's the power of levers!

Numerical 2 — Pulley Efficiency

A single movable pulley is used to lift a load of 100 kgf. The effort required is 55 kgf. Find MA, VR, and efficiency.

MA = L / E = 100 / 55 = 1.82 For a single movable pulley, VR = 2 (2 rope segments support the load) η = MA / VR = 1.82 / 2 = 0.91 = 91%

Numerical 3 — Block and Tackle

A block and tackle system has 4 pulleys in each block (total 4 rope segments supporting the load). A load of 200 kgf is lifted with an effort of 60 kgf. Find MA, VR, and efficiency.

MA = L / E = 200 / 60 = 3.33 VR = number of rope segments = 4 η = MA / VR = 3.33 / 4 = 0.833 = 83.3% Work input = E × d_E, Work output = L × d_L If load rises 1 m, effort moves 4 m (since VR = 4)

Numerical 4 — MA from Lever Diagram

In a pair of scissors, the load arm is 4 cm and the effort arm is 12 cm. Find its MA. Is it a force multiplier or speed multiplier?

MA = Effort arm / Load arm = 12 / 4 = 3 MA > 1 → it's a force multiplier

Fun fact: Scissors are actually two Class I levers joined together. Most scissors have MA > 1 so cutting is easier.

12) Quick Revision — Night Before the Exam

MA = L/E — ratio of load to effort (no unit)
VR = d_E / d_L — ratio of distances (design-dependent)
Efficiency η = MA/VR — always < 1 for real machines
Ideal machine: MA = VR, η = 100%
Principle of machine: Work input = Work output (ideal)
Levers: Class I (fulcrum middle), Class II (load middle, MA>1), Class III (effort middle, MA<1)
Single fixed pulley: MA = VR = 1 (changes direction only)
Single movable pulley: MA = VR = 2 (multiplies force by 2)
Block and tackle: VR = number of rope segments supporting the movable block

Common mistakes: (1) Forgetting that efficiency has no unit — it's a ratio or percentage. (2) Writing MA = Effort arm/Load arm for levers but then using the same formula for pulleys — no, for pulleys find MA from L/E. (3) Confusing load arm and effort arm — always measure from the fulcrum. (4) For block and tackle, count only the segments that directly support the movable block.

For lever numericals: MA = Effort Arm / Load Arm is the fastest way. Just find the two distances from the fulcrum, divide, and you're done. For pulley numericals: find VR first (count rope segments), then find MA using L/E, then get η. This order never fails.

13) All Formulas at One Glance

MA = Load / Effort = L / E VR = d_E / d_L Efficiency η = Work output / Work input = MA / VR η% = (MA / VR) × 100% For levers: MA = Effort arm / Load arm For ideal machine: MA = VR For block and tackle: VR = n (number of rope segments) Work input = E × d_E Work output = L × d_L Wasted work = Work input - Work output