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 how energy is stored and transferred in moving objects, elevated objects, and compressed springs using real-world examples
- Define kinetic energy, gravitational potential energy, and elastic potential energy with precise IB-aligned notation
- Derive the expressions for kinetic energy and gravitational potential energy from first principles using Newton's laws and kinematics
- Apply the principle of conservation of mechanical energy to solve figure-based and graph-based problems
- Analyse energy–displacement and energy–time graphs to identify transformations between energy forms
- Evaluate common misconceptions about energy and connect mechanical energy concepts to the wider IB Physics course
🌍 Real-World Context Watch a roller coaster climb slowly to the top of its first hill, then plunge downward at breathtaking speed. At the peak, the car moves sluggishly — yet moments later it races through the valley below. No engine is pushing it down; the energy was already there, stored silently in the car's elevated position. The same principle governs a diver leaping from a board, a bow launching an arrow, and a bungee jumper bouncing at the end of an elastic cord. In each case, energy changes its form — from stored to moving, from moving to stored — yet something remarkable remains constant throughout. Understanding what that something is, and why it is conserved, is the heart of this topic.
🔍 Guiding Question How can we use the concept of energy to predict the speed of an object at any point along its path, without needing to know the details of every force acting on it at every instant?
Physical Setup and Diagrams
Consider three everyday systems: a ball thrown upward, a spring compressed against a wall, and a pendulum swinging back and forth. In each case, an object possesses energy by virtue of its motion, its position, or its deformation. As the system evolves, these quantities change — the ball slows as it rises, the spring pushes the ball forward as it expands, the pendulum trades height for speed. Yet in each system, if we add up all the energy contributions at any moment, we obtain the same total. This is the central observation that motivates the study of mechanical energy.
Notice that in every panel of the diagram, the energy is never created or destroyed — it simply moves between forms. When the ball is at its highest point, all its mechanical energy is stored as gravitational potential energy; when it returns to ground level, all that energy has converted back to kinetic energy. The spring stores energy in its deformation; the pendulum stores energy in its height. The total mechanical energy — the sum of all these contributions — remains constant throughout, provided no non-conservative forces (such as friction or air resistance) do work on the system.
Core Concepts and Definitions
Before we can write any equations, we need to build a clear picture of what each form of energy actually means physically. Energy is not a substance — it is a scalar quantity that describes the capacity of a system to do work. When a moving car collides with a stationary one, it transfers energy through the collision; when a stretched elastic band is released, it transfers energy to the projectile it launches. In each case, the energy was stored in a particular form and then converted into another form or transferred to another object.
📖 Key Definition — Kinetic Energy The kinetic energy \( E_k \) of an object is the energy it possesses by virtue of its motion. It depends on the mass of the object and the square of its speed. Kinetic energy is a scalar quantity measured in joules (J).
The key insight about kinetic energy is that it depends on the square