1. Simple Machines 🔧
Simple machines make work easier by changing the magnitude or direction of force. These are the building blocks of all complex machinery.
| Simple Machine | How It Works | Mechanical Advantage | Examples |
|---|---|---|---|
| Lever | Rigid bar rotating around a fulcrum | MA = effort arm / load arm | Seesaw, crowbar, scissors |
| Pulley | Wheel with rope that changes force direction | MA = number of supporting ropes | Flagpole, crane, well bucket |
| Wheel & Axle | Larger wheel attached to smaller axle | MA = wheel radius / axle radius | Doorknob, steering wheel, screwdriver |
| Inclined Plane | Sloped surface to raise objects | MA = length / height | Ramp, slide, stairs |
| Wedge | Two inclined planes joined together | MA = length / thickness | Knife, axe, nail, chisel |
| Screw | Inclined plane wrapped around cylinder | MA = circumference / pitch | Bolt, jar lid, spiral staircase |
Three Classes of Levers:
Class 1:
Fulcrum in middle
Load—Fulcrum—Effort
Examples: Seesaw, scissors
Class 2:
Load in middle
Fulcrum—Load—Effort
Examples: Wheelbarrow, nutcracker
Class 3:
Effort in middle
Fulcrum—Effort—Load
Examples: Tweezers, fishing rod
2. Gears & Gear Systems ⚙️
Gears transfer motion and force between rotating shafts. Understanding gear relationships is essential for mechanical reasoning.
| Concept | Rule | Formula |
|---|---|---|
| Direction | Meshing gears rotate in OPPOSITE directions | If A turns clockwise, B turns counterclockwise |
| Gear Ratio | Teeth on driven gear ÷ teeth on driving gear | GR = T₂ / T₁ |
| Speed | Smaller gear turns FASTER | n₁ × T₁ = n₂ × T₂ |
| Torque | Larger gear produces MORE torque | Torque ∝ Gear size |
| Idler Gear | Changes direction only, not speed/torque | Odd number of gears = same direction |
💡 Quick Rule:
Small → Large gear: Speed decreases, Torque increases (good for lifting)
Large → Small gear: Speed increases, Torque decreases (good for fans)
3. Pulley Systems 🏗️
Pulleys change force direction and can provide mechanical advantage when combined.
Fixed Pulley:
- Attached to ceiling/support
- Changes force DIRECTION only
- MA = 1 (no force advantage)
- Example: Flagpole
Movable Pulley:
- Moves with the load
- Reduces force needed by HALF
- MA = 2
- Example: Block and tackle
Calculating Pulley MA:
Count the number of rope segments supporting the load!
- 1 rope segment = MA of 1 (fixed pulley)
- 2 rope segments = MA of 2
- 4 rope segments = MA of 4
Force needed = Weight / MA
4. Forces & Equilibrium ⚖️
Understanding how forces balance is crucial for mechanical reasoning problems.
| Concept | Definition | Application |
|---|---|---|
| Equilibrium | Net force = 0, object doesn't move | Balanced seesaw, hanging weights |
| Torque (Moment) | Force × Distance from pivot | Lever problems, rotating objects |
| Center of Gravity | Point where weight is concentrated | Balance point, stability |
| Friction | Force opposing motion between surfaces | Braking, grip, energy loss |
🔄 Moment Balance (Seesaw Rule):
Weight₁ × Distance₁ = Weight₂ × Distance₂
For a balanced lever, clockwise moments = counterclockwise moments
5. Fluid Mechanics & Pressure 💧
Understanding how fluids behave and transmit pressure is essential for hydraulics and pneumatics.
Key Concepts:
- Pressure: Force per unit area (P = F/A)
- Pascal's Law: Pressure transmits equally in all directions
- Hydraulic Press: Small force on small piston = large force on large piston
- Buoyancy: Upward force on submerged objects
Hydraulic Advantage:
F₂/F₁ = A₂/A₁
Larger piston area = larger output force
Examples: Car brakes, hydraulic lifts, bulldozers
6. Electrical Circuits Basics ⚡
Basic electrical concepts often appear in mechanical-technical sections.
| Circuit Type | Current | Voltage | Characteristics |
|---|---|---|---|
| Series | Same everywhere | Splits among components | One path; if one breaks, all stop |
| Parallel | Splits among branches | Same across branches | Multiple paths; others work if one breaks |
Ohm's Law: V = IR
- V = Voltage (Volts)
- I = Current (Amperes)
- R = Resistance (Ohms)
7. Practice Questions 📝
Question 1: Gear Direction
Gear A (20 teeth) turns clockwise and meshes with Gear B (40 teeth). In which direction does Gear B turn, and what is its speed relative to A?
Answer: Gear B turns counterclockwise (opposite to A). Speed = half of A (because B has twice the teeth, it rotates half as fast).
Question 2: Pulley System
A 100 kg weight is lifted using a pulley system with 4 rope segments supporting the load. What force is needed? (g = 10 m/s²)
Solution: Weight = 100 × 10 = 1000 N. MA = 4.
Force = 1000 / 4 = 250 N
Answer: 250 N (or 25 kg-force)
Question 3: Lever Balance
A seesaw has a 30 kg child sitting 2 meters from the fulcrum. Where should a 20 kg child sit to balance?
Solution: 30 × 2 = 20 × d
d = 60 / 20 = 3 meters
Answer: 3 meters from the fulcrum on the opposite side
Question 4: Inclined Plane
A ramp is 6 meters long and 2 meters high. What is the mechanical advantage?
Solution: MA = Length / Height = 6 / 2 = 3
Answer: MA = 3 (you need only 1/3 of the direct lifting force)
Question 5: Hydraulics
A hydraulic press has a small piston of area 10 cm² and large piston of area 100 cm². If 50 N force is applied to the small piston, what force is produced at the large piston?
Solution: F₂/F₁ = A₂/A₁
F₂ = F₁ × (A₂/A₁) = 50 × (100/10) = 50 × 10 = 500 N
Answer: 500 N