Work, Energy, and Simple Machines

Introduction
In everyday language we use "work" and "energy" loosely. In physics these terms have precise meanings. Understanding how work transfers energy, how energy transforms, and how simple machines help us do tasks with less effort are essential concepts in physics.

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Key Concepts

• 1. Work
• Work (W) is done when a force causes displacement in the direction of the force.
• W = F x s x cos(theta)
• where F = applied force, s = displacement, theta = angle between force and displacement.
• If force and displacement are in the same direction: theta = 0, cos(0) = 1, so W = F x s.
• If force is perpendicular to displacement: theta = 90, cos(90) = 0, so W = 0 (no work done).
• SI unit: Joule (J). 1 J = 1 N x 1 m = 1 N m.
• Work is a scalar quantity.

• 2. Energy
• Energy is the capacity to do work. SI unit: Joule (J).
• Main forms relevant here:
• Kinetic Energy (KE): energy of motion. KE = (1/2)mv²
• Potential Energy (PE): stored energy due to position or configuration.
• Gravitational PE: PE = mgh (m = mass, g = 9.8 m/s², h = height above reference).
• Mechanical Energy = KE + PE

3. Work-Energy Theorem
The net work done on an object equals the change in its kinetic energy.
W_net = change in KE = (1/2)mv² - (1/2)mu² = (1/2)m(v² - u²)

• 4. Law of Conservation of Energy
• · Energy cannot be created or destroyed. It can only be converted from one form to another. The total energy of a closed system remains constant. ·
• Example: a pendulum swings — KE converts to PE at the top; PE converts back to KE at the bottom. In absence of friction, total mechanical energy stays constant.
• At maximum height: all PE, zero KE.
• At lowest point: all KE, zero PE.

• 5. Power
• Power (P) is the rate of doing work (or transferring energy).
• P = W / t = F x v (when force and velocity are in the same direction)
• SI unit: Watt (W). 1 W = 1 J/s.
• 1 kilowatt (kW) = 1000 W
• Horsepower (hp): 1 hp = 746 W (not SI but commonly used).
• Commercial unit of energy: 1 kWh (kilowatt-hour) = 1000 x 3600 J = 3.6 x 10⁶ J = 3.6 MJ.

6. Simple Machines
A simple machine is a device that makes work easier by changing the magnitude or direction of a force. Key principle: work in = work out (in an ideal, frictionless machine).

Mechanical Advantage (MA) = Load / Effort = output force / input force
Velocity Ratio (VR) = distance moved by effort / distance moved by load
Efficiency = (MA / VR) x 100% = (Work output / Work input) x 100%

• Types of simple machines:
• Lever: a rigid bar pivoting on a fulcrum. Three classes based on position of fulcrum, effort, and load. Example: see-saw (Class 1), wheelbarrow (Class 2), tweezers (Class 3).
• Pulley: a wheel with a rope. Single fixed pulley changes direction; compound pulleys reduce effort.
• Inclined plane: a sloping surface; reduces effort needed to raise an object. MA = length/height.
• Wheel and axle: large wheel with small axle; e.g., steering wheel, screwdriver.
• Screw: inclined plane wrapped around a cylinder.
• Wedge: two inclined planes joined; e.g., axe, knife.

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Worked Examples

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