Preview
IB DP Physics — Unit A: Space, Time and Motion | SL & HL | A.3 Work, Energy and Power
📋 What You Will Learn
- Observe and describe real-world energy transfers and identify why some machines are more effective than others at converting energy
- Define power, efficiency, and energy density with precise IB-aligned language and correct SI units
- Derive the relationship between power, force, and velocity from the definition of work done
- Apply power and efficiency equations to solve figure-based and graph-based problems involving motors, engines, and energy sources
- Analyse force–displacement and power–time graphs to extract energy and efficiency information
- Evaluate the significance of energy density when comparing fuels and energy storage technologies
🌍 Real-World Context When a Formula 1 car accelerates from rest to 100 km h⁻¹ in under 2.5 seconds, its engine is delivering an enormous amount of energy in a very short time. Yet despite this impressive performance, only about 40–45% of the chemical energy stored in the fuel is actually converted into useful kinetic energy — the rest is lost as heat through the exhaust and friction. Meanwhile, engineers designing electric vehicles obsess over a different quantity: how much energy can be stored per kilogram of battery material. These three ideas — how fast energy is delivered, how much is usefully converted, and how much can be stored — are the foundations of power, efficiency, and energy density, and they shape every energy technology from smartphones to power stations.
🔍 Guiding Question How do the concepts of power, efficiency, and energy density allow us to compare and evaluate different energy sources and machines, and what are the physical limits on how efficiently energy can be transferred?
Physical Setup and Diagram
Consider a motor lifting a heavy crate vertically upward at a steady speed. The motor does work against gravity, transferring electrical energy into gravitational potential energy of the crate. However, not all of the electrical energy supplied to the motor ends up as gravitational potential energy — some is dissipated as heat in the motor windings and as sound. The rate at which the motor supplies energy, the fraction of that energy usefully transferred, and the amount of energy available per kilogram of fuel powering the motor are three distinct but deeply connected physical quantities.
Notice from the diagram that energy is conserved overall — the total energy input equals the sum of useful output and wasted energy. What varies between different motors is the proportion of input energy that becomes useful output. A more efficient motor wastes less energy as heat and delivers more to the crate. The rate at which this energy transfer occurs — regardless of efficiency — is what we call power.
Core Concepts and Definitions
Imagine two workers moving identical boxes up a flight of stairs. The first worker takes 10 seconds; the second takes 20 seconds. Both do the same total work against gravity — they lift the same mass through the same height — but the first worker does it in half the time. Physically, something is different: the first worker is transferring energy more rapidly. This rate of energy transfer is what physicists call power.
📖 Key Definition — Power Power is the rate at which work is done or energy is transferred. It is defined as the work done per unit time: \( P = \frac{W}{t} \), where \( W \) is the work done in joules and \( t \) is the time taken in seconds. The SI unit of