Work and conservation of energy: (c) the principle of conservation of energy

The idea

The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred from one form to another or from one place to another. The total energy of a closed system remains constant. In mechanics, this means that when energy is transferred between stores, the total before and after is the same, provided no energy is transferred to or from outside the system. For example, a falling ball transfers gravitational potential energy to kinetic energy; if air resistance is negligible, the decrease in potential energy equals the increase in kinetic energy. If friction or air resistance acts, some energy is transferred to thermal energy, but the total energy is still conserved. This principle allows you to set up energy balance equations and solve for unknown speeds, heights or energy transfers.

What earns the marks

• State that energy cannot be created or destroyed, only transferred between forms or stores.
• State that the total energy of a closed system is constant.
• Apply conservation of energy by equating total energy before and after a process, accounting for all energy transfers.
• Recognise that in the absence of resistive forces, gravitational potential energy lost equals kinetic energy gained for a falling object.
• Recognise that when resistive forces act, some energy is transferred to thermal energy, but the total energy is still conserved.
• Use the principle to set up equations such as mgh = ½mv² for a falling object with no air resistance.
• Identify the system and check whether energy is transferred across its boundary before applying conservation.

Common mistakes and how to put them right

• Thinking that energy is 'used up' or disappears.

  Put it right by stating that energy is transferred to other forms, often thermal energy to the surroundings.

• Applying conservation of energy without including all energy transfers, such as ignoring thermal energy when friction is present.

  Put it right by listing all energy stores and transfers.

• Assuming that mechanical energy (kinetic plus potential) is always conserved.

  Put it right by noting that it is only conserved when resistive forces do no work.

• Confusing conservation of energy with conservation of momentum.

  Put it right by keeping the two principles separate and applying each where appropriate.

• Forgetting that the principle applies to a closed system.

  Put it right by defining the system and checking for external energy transfers.

Exam tips

• State the principle in full when asked, using the wording 'energy cannot be created or destroyed, only transferred'.
• When solving problems, write an energy balance equation: total energy before = total energy after, including all forms.
• If a process involves friction or air resistance, include a thermal energy term in your equation.
• Check that your answer is physically sensible: for example, a speed calculated from energy conservation should not exceed the speed of light or be negative.