How does the law of conservation of energy apply to closed systems?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed in a closed system.

In a closed system, the total amount of energy remains constant. This is the fundamental principle of the law of conservation of energy. It means that energy can change from one form to another (for example, from potential energy to kinetic energy), but the total energy within the system will always remain the same. This is because, in a closed system, no energy is allowed to enter or leave.

Let's consider a simple example of a swinging pendulum. At the highest point of its swing, the pendulum has maximum potential energy and zero kinetic energy. As it begins to swing down, the potential energy is converted into kinetic energy. At the lowest point of its swing, the pendulum has maximum kinetic energy and zero potential energy. As it swings back up, the kinetic energy is converted back into potential energy. Throughout this process, the total energy of the system (the sum of the potential and kinetic energy) remains constant.

Another example is a roller coaster. At the top of a hill, the roller coaster car has a large amount of potential energy due to its height. As it descends, this potential energy is converted into kinetic energy, causing the car to speed up. As the car climbs the next hill, the kinetic energy is converted back into potential energy, causing the car to slow down. Again, the total energy of the system remains constant.

In both these examples, energy is not lost but merely changes form. This is the essence of the law of conservation of energy. It's important to note that this law only applies to closed systems, where no energy is added or removed. In real-world situations, some energy is often lost to the surroundings as heat or sound, making the system not perfectly closed. However, for the purposes of studying physics at IGCSE level, we often simplify scenarios to consider them as closed systems.