Conservation of energy Revision Notes

The Efficiency Equation

Efficiency is calculated using the formula: efficiency = (useful energy transferred by the device / total energy supplied to the device). This can be expressed as a decimal (between 0 and 1) or as a percentage (by multiplying the decimal by 100). Both the useful energy and total energy must be in the same units, typically Joules (J).

Understanding Energy Transfer and Losses

In any energy transfer, not all the energy supplied is converted into the desired useful form. Some energy is always dissipated or 'wasted', usually into the surroundings as heat or sound, due to inefficiencies in the device. For example, in an incandescent light bulb, a significant portion of the electrical energy supplied is converted into heat rather than light, making it less efficient than an LED bulb.

Applying the Efficiency Formula

To apply the formula, identify the useful energy output and the total energy input. For example, if a motor is supplied with electrical energy and produces kinetic energy, the kinetic energy is the useful output. Any energy not converted into kinetic energy is wasted, often as heat. Knowing any two of the three variables (efficiency, useful energy, total energy) allows you to calculate the third by rearranging the equation.

Calculating Change in Gravitational Potential Energy

The change in gravitational potential energy (∆GPE) can be calculated using the equation: ∆GPE = m × g × ∆h.

• ∆GPE is the change in gravitational potential energy, measured in joules (J).
• m is the mass of the object, measured in kilograms (kg).
• g is the gravitational field strength, measured in newtons per kilogram (N/kg).
• ∆h is the change in vertical height, measured in metres (m).

Units and Constants

It's vital to use consistent SI units for all quantities in the equation. Mass must be in kilograms (kg), height in metres (m), and gravitational field strength in newtons per kilogram (N/kg). On Earth, the gravitational field strength (g) is approximately 9.8 N/kg, but for many calculations in physics, it is often approximated as 10 N/kg for simplicity, unless specified otherwise. This approximation makes calculations easier without significantly affecting the understanding of the concept.

Real-world Applications of GPE

The concept of GPE is fundamental in many real-world applications. For instance, dams store water at a high elevation, converting the water's GPE into mechanical or electrical energy as it flows downwards. Roller coasters gain GPE as they are pulled to the top of a hill, which is then converted into kinetic energy for the thrilling ride. Lifting weights in a gym increases their GPE, and this energy can then be used to do work when the weights are lowered slowly.