Energy Stores, Transfers and Work
Energy Stores and Conservation
The law of conservation of energy is one of the most fundamental principles in physics: energy cannot be created or destroyed — only transferred between stores. In any closed system, the total energy before a process equals the total energy after. Energy that appears to 'disappear' has been dissipated — spread out into thermal energy in the surroundings where it cannot easily be recovered.
There are eight main energy stores: kinetic (moving objects), gravitational potential (objects at height), elastic potential (stretched or compressed materials), chemical (food, fuels, batteries), thermal (hot objects), magnetic, electrostatic and nuclear. Energy transfers between stores via four pathways: heating, radiation, electrical working, and mechanical working.
Energy cannot be created or destroyed. It transfers between stores (kinetic, gravitational potential, elastic, chemical, thermal, and others). Any energy that is 'wasted' is dissipated as thermal energy in the surroundings.
Work Done
When a force moves an object through a distance, work is done. Work done equals the energy transferred. The equation is:
$$W = F \times d$$
Where \(W\) is work done in joules (J), \(F\) is force in newtons (N), and \(d\) is distance moved in the direction of the force in metres (m). One joule of work is done when a force of 1 N moves an object 1 m. Work done and energy transferred are equivalent — both are measured in joules.
Example: a person pushes a shopping trolley with 40 N of force across 5 m. Work done = \(40 \times 5 = 200\) J. This energy is transferred from the person's chemical energy store into the kinetic energy of the trolley (and some to thermal energy through friction with the floor).
Question: A builder lifts bricks weighing 600 N to a scaffold 4 m above the ground. How much work is done?
Step 1: Identify equation: \(W = F \times d\)
Step 2: Substitute: \(W = 600 \times 4 = 2400 \text{ J}\)
Interpretation: This 2 400 J has been transferred from the builder's chemical energy store into the gravitational potential energy store of the bricks.
Kinetic and Gravitational Potential Energy
A moving object stores kinetic energy (KE):
$$KE = \frac{1}{2} \times m \times v^2$$
Where \(m\) is mass in kg and \(v\) is speed in m/s. Notice that KE depends on \(v^2\) — doubling speed quadruples kinetic energy. This is why road speed limits have such a large effect on collision severity.
An object at height stores gravitational potential energy (GPE):
$$GPE = m \times g \times h$$
Where \(m\) is mass (kg), \(g\) is gravitational field strength (10 N/kg on Earth's surface), and \(h\) is height (m). A 3 kg book placed on a shelf 1.5 m high gains GPE = \(3 \times 10 \times 1.5 = 45\) J relative to the floor.
When an object falls freely (ignoring air resistance), GPE converts into KE. At the start all energy is stored as GPE; at the bottom all has converted to KE. At any point in between, total energy = GPE + KE = constant. This allows you to calculate the speed of a falling object using \(GPE_{lost} = KE_{gained}\), i.e. \(mgh = \frac{1}{2}mv^2\). The masses cancel, giving \(v = \sqrt{2gh}\).
Example: A ball dropped from 5 m above the ground (ignoring air resistance): \(v = \sqrt{2 \times 10 \times 5} = \sqrt{100} = 10 \text{ m/s}\) just before hitting the ground. In reality, air resistance dissipates some energy as thermal energy in the air, so the actual speed would be slightly less.
Efficiency
No device transfers energy with 100% efficiency — some is always dissipated as wasted thermal energy. Efficiency is calculated as:
$$\text{Efficiency} = \frac{\text{useful output energy}}{\text{total input energy}}$$
Efficiency can be expressed as a decimal (0 to 1) or multiplied by 100 to give a percentage. A motor that receives 400 J of electrical energy and performs 280 J of useful work has efficiency = \(\frac{280}{400} = 0.70\) = 70%. The remaining 120 J is wasted as heat and sound. Engineers improve efficiency through lubrication (reducing friction), streamlining (reducing air resistance) and thermal insulation.
Efficiency = useful output energy ÷ total input energy. No device is 100% efficient. KE = ½mv² and GPE = mgh are the two key energy store equations — both appear regularly in exam calculations.