Machines notes: ICSE Class 10 Physics (Science Paper 1)

1. Machines: MA, VR and efficiency

Load (L): force overcome; effort (E): force applied.
$\text{MA} = L/E$ ; $\text{VR} = d_E/d_L$ (no units).
Work input $= E d_E$ ; output $= L d_L$ ; $\eta = \dfrac{L d_L}{E d_E} = \dfrac{\text{MA}}{\text{VR}}$ .
Ideal machine: $\eta = 1$ , MA = VR. Practical: friction and weight of moving parts → $\eta < 1$ , MA < VR.
Uses: force multiplier (MA > 1), speed multiplier (MA < 1), change of direction, convenient point of application.

Table contrasting ideal and practical machines
Machine	MA	VR	η
Ideal	VR	VR	1
Practical	< VR	VR	< 1

Formulas

Efficiency
$\eta = \dfrac{\text{MA}}{\text{VR}}$

Key terms

Mechanical advantage: The ratio of the load to the effort.
Velocity ratio: The ratio of the distance moved by the effort to the distance moved by the load in the same time.
Efficiency: The ratio of the useful work output to the work input of a machine.

2. Levers

Rigid bar turning about a fulcrum. Principle: $L \times \text{load arm} = E \times \text{effort arm}$ , so ideal $\text{MA} = \dfrac{\text{effort arm}}{\text{load arm}}$ .

Class	In the middle	MA	Examples
I	Fulcrum	> 1, = 1 or < 1	See-saw, scissors, crowbar, beam balance
II	Load	Always > 1	Nutcracker, wheelbarrow, bottle opener
III	Effort	Always < 1	Forceps, sugar tongs, fishing rod

Class III levers sacrifice force for speed and distance.

Table of three levers and their classes
Lever	Class
Scissors	I
Nutcracker	II
Forceps	III

Formulas

Ideal lever
$\text{MA} = \dfrac{\text{effort arm}}{\text{load arm}}$

Key terms

Fulcrum: The fixed point about which a lever turns.
Effort arm: The perpendicular distance of the effort from the fulcrum.

3. Levers in the human body

Action	Fulcrum	Load	Effort	Class
Nodding	Top of spine	Weight of face	Neck muscles	I
Raising heels	Toes	Body weight at ankle	Calf muscle	II
Lifting with forearm	Elbow	Weight in hand	Biceps	III

Table of body levers
Body part	Class
Neck	I
Foot	II
Forearm	III

Key terms

Biceps lever: The forearm used as a class III lever, with the biceps pulling between the elbow and the hand.

4. Pulley systems

Single fixed pulley: MA = VR = 1 (ideal); changes direction of effort (pull down using body weight).
Single movable pulley: VR = 2; with pulley weight $w$ : $2E = L + w$ .
Block and tackle: VR = $n$ = number of strands supporting the lower block. No friction: $nE = L + w$ , $\text{MA} = \dfrac{nL}{L + w}$ , $\eta = \dfrac{L}{L + w}$ .
MA < VR because of friction and the weight of the lower block; efficiency rises with larger load.

Table of pulley systems
System	VR	Ideal MA
Fixed pulley	1	1
Movable pulley	2	2
Block and tackle	n	n

Formulas

Block and tackle without friction
$nE = L + w$
Efficiency without friction
$\eta = \dfrac{L}{L + w}$

Key terms

Block and tackle: A pulley system with a fixed upper block and a movable lower block joined by one continuous string.

Exam tips

Common mistakes

Giving units to MA or VR.
Efficiency greater than 1.
Counting strands attached to the upper block.
Forgetting the weight of the lower block.

How marks are usually awarded

Definitions (1 mark each).
Derivation η = MA/VR (2 marks).
Pulley numericals (1 mark each): VR, effort from nE = L + w, MA, efficiency.

1. Machines: MA, VR and efficiency

Formulas

Key terms

2. Levers

Formulas

Key terms

3. Levers in the human body

Key terms

4. Pulley systems

Formulas

Key terms

Exam tips

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