Changes in Energy

Energy Changes Overview

When energy changes occur in a system, energy is transferred from one form to another or from one place to another. The total amount of energy before and after the change remains the same, but the form of energy involved can be different.

Common forms of energy involved in changes include:

• Kinetic energy (energy of movement)
• Potential energy (energy stored due to position or configuration)
• Elastic potential energy (energy stored when objects are stretched or compressed)
• Thermal energy (energy related to temperature)

Energy changes happen in everyday situations, such as when a moving car slows down (kinetic energy decreases) or when a stretched spring returns to its original shape (elastic potential energy changes).

Types of Energy Changes

Kinetic and Potential Energy Changes

Kinetic energy is the energy an object has because of its motion. It depends on the mass and speed of the object. Potential energy is energy stored in an object due to its position or height. (Gravitational potential energy is covered in another topic.)

When an object moves, energy can change between kinetic and potential forms. For example, a ball thrown upwards slows down as kinetic energy converts into gravitational potential energy.

The formula for kinetic energy is:

$$\text{Kinetic Energy} = \frac{1}{2} m v^2$$

where $m$ is mass in kilograms and $v$ is velocity in metres per second.

For example, a 2 kg ball moving at 3 m/s has kinetic energy:

$$KE = \frac{1}{2} \times 2 \times 3^2 = 9 \text{ J}$$

Elastic Potential Energy Changes

Elastic potential energy is stored when objects like springs or elastic bands are stretched or compressed. The energy is stored because the object is under tension or compression.

The amount of elastic potential energy stored depends on how far the object is stretched or compressed.

The elastic potential energy stored in a spring can be calculated by:

$$E = \frac{1}{2} k e^2$$

where $k$ is the spring constant (N/m) and $e$ is the extension (m).

For example, if a spring with a spring constant of 200 N/m is stretched by 0.05 m, the elastic potential energy stored is:

$$E = \frac{1}{2} \times 200 \times 0.05^2 = 0.25 \text{ J}$$

Thermal Energy Changes

Thermal energy is the energy an object has due to the movement of its particles. When energy is transferred to an object by heating, its thermal energy increases, causing a rise in temperature. (Energy transfer by conduction, convection, and radiation is covered in other topics.)

Thermal energy changes often happen when work is done against friction or when electrical energy is converted into heat.

For example, rubbing your hands together transfers mechanical energy into thermal energy, warming your skin.

Energy Transfer Methods

Mechanical Work

Mechanical work transfers energy when a force moves an object through a distance. The energy transferred depends on the size of the force and the distance moved in the direction of the force.

Work done (energy transferred) is calculated by:

$$W = F \times d$$

where $W$ is work done in joules (J), $F$ is force in newtons (N), and $d$ is distance in metres (m).

For example, if a person pushes a box with a force of 10 N for 3 m, the energy transferred by mechanical work is:

$$W = 10 \times 3 = 30 \text{ J}$$

Heating

Heating transfers energy from a hotter object to a cooler one, increasing the thermal energy of the cooler object.

For example, placing a metal spoon in hot water causes energy transfer by heating, warming the spoon.

Electrical Transfer

Electrical energy transfer happens when an electric current flows through a component, transferring energy to the component.

For example, in an electric heater, electrical energy is transferred to thermal energy, warming the room.

Energy Conservation in Changes

Energy cannot be created or destroyed; it can only be transferred from one form to another or from one place to another. This is the principle of conservation of energy.

In any energy change, the total energy before the change equals the total energy after the change.

However, not all energy transferred is useful. Some energy is dissipated, meaning it spreads out and becomes less useful, often as thermal energy due to friction or resistance.

For example, when a car brakes, kinetic energy is transferred to thermal energy in the brakes, which is dissipated to the surroundings and cannot be used to move the car.

For instance, when a cyclist pedals uphill, chemical energy from food is transferred to kinetic energy and gravitational potential energy. Some energy is dissipated as thermal energy due to friction between the bike and road.