Chapter 6 : Work and Energy

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Chapter Overview & SLOs

What is work in physics? Chapter 6, "Work and Energy," explores the fundamental concepts of physical effort and the capacity of systems to perform tasks. This chapter answers fundamental questions about how work is calculated, what energy is, and how they are related. How is work defined and calculated? You will learn that work is defined as the product of force and displacement in the direction of the force: - Formula: $W = Fd \cosθ$ (Work = Force × Displacement × cosine of angle between force and displacement) - SI Unit: Joule (J) = N·m - Conditions for work: - Maximum work: When force is parallel to displacement ($θ = 0°$), $\cos0° = 1$, so $W = Fd$ (maximum) - Zero work: When force is perpendicular to displacement ($θ = 90°$), $\cos90° = 0$, so $W = 0$. Example: Centripetal force on an orbiting satellite (force toward center, displacement tangential, no work done) - Negative work: When force opposes displacement ($θ = 180°$), $\cos180° = -1$, so $W = -Fd$. Example: Friction force opposing motion - Minimum work (not zero): When force is at any angle other than 0°, 90°, or 180°, work is between 0 and Fd What is kinetic energy and how is it derived? You will study kinetic energy - the energy possessed by a moving object: - Formula: $KE = \frac{1}{2}mv^2$ - Derivation using graphical method: For an object accelerating from rest under constant force F, work done = area under force-displacement graph = $F × d$. Using $F = ma$ and $v^2 = 2ad$, we get $d = v^2/2a$, so $W = m × a × (v^2/2a) = \frac{1}{2}mv^2$. Therefore, $KE = \frac{1}{2}mv^2$. - Key point: Doubling velocity increases kinetic energy by a factor of 4 (since $v^2$ is involved) What is potential energy and how is it derived? You will learn about gravitational potential energy - energy stored due to an object's position in a gravitational field: - Formula: $PE = mgh$ (Potential energy = mass × gravitational acceleration × height) - Derivation: To lift an object from ground to height h, force required = weight = mg. Work done = Force × displacement = $mg × h$. This work is stored as potential energy, so $PE = mgh$. - Reference point: Potential energy is relative; we usually take ground level as zero (h = 0, PE = 0) What is the law of conservation of energy? A significant focus is placed on the Law of Conservation of Energy: - Statement: Energy cannot be created or destroyed, only transformed from one form to another. Total energy in an isolated system remains constant. - Falling ball example: At height h, PE = mgh, KE = 0. During fall, PE decreases, KE increases. Just before hitting ground, PE = 0, KE = mgh = $\frac{1}{2}mv^2$ - Pendulum example: At extreme positions, PE = max, KE = 0. At lowest point, KE = max, PE = min (but not zero if reference is lowest point) - Hydroelectric power station: Potential energy of water stored in dam → kinetic energy of flowing water → mechanical energy of turbine → electrical energy (generator) - Energy transformations in nature: Solar energy (sun) → chemical energy (plants via photosynthesis) → chemical energy (animals eating plants) → kinetic energy (animal movement) → heat energy (metabolism) What are renewable and non-renewable energy resources? The chapter categorizes energy resources: - Renewable Energy Resources (can be replenished naturally within human lifetime): - Solar Energy: Energy from sun via solar panels (photovoltaic cells) or thermal collectors - Wind Energy: Kinetic energy of wind turns wind turbines to generate electricity - Ocean Energy: Tidal energy (from tides), wave energy (from ocean waves) - Geothermal Energy: Heat from Earth's interior used for heating and electricity generation - Biomass Energy: Energy from organic matter (wood, agricultural waste, biogas) - Hydropower: Energy from flowing water (dams, run-of-river) - Advantages: Clean (no pollution), sustainable, infinite supply - Disadvantages: Intermittent (sun doesn't always shine, wind doesn't always blow), high initial cost - Non-Renewable Energy Resources (finite, cannot be replenished quickly): - Fossil Fuels: Coal, oil (petroleum), natural gas. Formed from dead organisms millions of years ago. - Nuclear Energy: Energy from nuclear fission (splitting uranium atoms) or fusion - Advantages: High energy density, reliable (available 24/7) - Disadvantages: Pollution (CO₂, SO₂, NOₓ), greenhouse gases causing climate change, finite supply, environmental damage from extraction What is power and how is it calculated? You will learn about power: - Definition: Rate of doing work (time rate of energy transfer) - Formula: $P = \frac{W}{t} = \frac{ΔE}{t}$ (Power = Work / time = Energy change / time) - Alternative formula for constant velocity: $P = Fv$ (Power = Force × velocity) - SI Unit: Watt (W) = J/s = N·m/s - Horsepower (hp): 1 hp = 746 W (often approximated as 745.7 W) - Example: A 100 W bulb converts 100 J of electrical energy into light and heat every second What is efficiency and why are machines never 100% efficient? Finally, you will learn about efficiency: - Formula: $\text{Efficiency} = \frac{\text{Useful Output Energy}}{\text{Total Input Energy}} × 100\%$ - Alternative formula: $\text{Efficiency} = \frac{\text{Useful Output Power}}{\text{Total Input Power}} × 100\%$ - Why efficiency is always less than 100%: Due to the Second Law of Thermodynamics, some energy is always "lost" as waste heat (thermal energy) that cannot be fully converted into useful work. Other losses include friction (converted to heat), sound, and light (where not intended). - Examples: Incandescent bulb efficiency ~5% (95% lost as heat), LED bulb efficiency ~40-50%, electric motor efficiency ~70-90%, car engine efficiency ~20-30% These notes are strictly aligned with the Student Learning Outcomes (SLOs) for the FBISE 2026 annual examination.

• What is work and its SI unit? Define work as the product of force and displacement in the direction of force (W = Fd cosθ) with SI unit Joule (J = N·m), and describe the conditions under which work is maximum (θ = 0°, force parallel to displacement), minimum (0 < work < Fd for angles between 0° and 90°), zero (θ = 90°, force perpendicular to displacement, e.g., centripetal force on satellite), and negative (θ = 180°, force opposes displacement).
• What are kinetic and potential energy? Differentiate between kinetic energy (energy due to motion, KE = ½mv²) and potential energy (energy due to position, P = mgh), and derive their mathematical expressions using graphical method (area under force-displacement graph for KE) and algebraic method (work against gravity for PE).
• What is the law of conservation of energy? Explain the law of conservation of energy (energy cannot be created or destroyed, only transformed from one form to another; total energy remains constant in isolated systems) and illustrate energy conversion processes in natural systems (falling ball, pendulum) and man-made systems (hydroelectric power station, where potential energy of water → kinetic energy → mechanical energy → electrical energy).
• What are renewable and non-renewable energy resources? Compare renewable energy resources (solar, wind, ocean/tidal, geothermal, biomass, hydropower - can be replenished naturally) and non-renewable energy resources (fossil fuels - coal, oil, natural gas, nuclear - finite and take millions of years to form), and evaluate their environmental and economic significance including pollution, greenhouse gases, and sustainability.

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