KE, GPE & EPE

Kinetic energy, gravitational potential energy, and elastic potential energy are all forms of energy stored in different ways: through motion, position in a gravitational field, and deformation of elastic objects, respectively.

Kinetic Energy (KE)

Kinetic energy is the energy an object has because of its motion. Any moving object stores kinetic energy.

The amount of kinetic energy depends on two factors:

• The mass of the object (how much matter it contains)
• The speed of the object (how fast it is moving)

The formula to calculate kinetic energy is:

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

• $m$ is the mass in kilograms (kg)
• $v$ is the speed in metres per second (m/s)
• $\text{KE}$ is the kinetic energy in joules (J)

Because speed is squared, increasing speed has a bigger effect on kinetic energy than increasing mass.

For example, a 2 kg ball moving at 3 m/s has kinetic energy $= 0.5 \times 2 \times 3^2 = 9 \text{ J}$.

For instance, if a car of mass 1000 kg is travelling at 20 m/s, its kinetic energy is:

$$\text{KE} = \frac{1}{2} \times 1000 \times 20^2 = 0.5 \times 1000 \times 400 = 200,000 \text{ J}$$

Gravitational Potential Energy (GPE)

Gravitational potential energy is the energy stored by an object because of its position in a gravitational field, usually related to its height above the ground.

The higher an object is lifted, the more gravitational potential energy it gains. Also, heavier objects have more gravitational potential energy at the same height.

The formula to calculate gravitational potential energy is:

$$\text{GPE} = mgh$$

• $m$ is the mass in kilograms (kg)
• $g$ is the gravitational field strength (usually $9.8 \text{ N/kg}$ on Earth)
• $h$ is the height above the ground in metres (m)
• $\text{GPE}$ is the gravitational potential energy in joules (J)

Note that $g$ is approximately 9.8 N/kg on Earth and may vary slightly depending on location.

For example, if a box of mass 5 kg is lifted 2 metres above the floor, its gravitational potential energy is:

$$\text{GPE} = 5 \times 9.8 \times 2 = 98 \text{ J}$$

Elastic Potential Energy (EPE)

Elastic potential energy is the energy stored in an elastic object when it is stretched or compressed.

Examples include springs, elastic bands, and bungee cords. The more you stretch or compress the object, the more energy is stored.

The formula to calculate elastic potential energy stored in a spring is:

$$\text{EPE} = \frac{1}{2} k e^2$$

• $k$ is the spring constant in newtons per metre (N/m), which measures the stiffness of the spring
• $e$ is the extension or compression of the spring from its natural length in metres (m)
• $\text{EPE}$ is the elastic potential energy in joules (J)

A higher spring constant means a stiffer spring that requires more force to stretch.

Note that this formula applies only when the spring is stretched or compressed within its elastic limit.

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:

$$\text{EPE} = \frac{1}{2} \times 200 \times (0.05)^2 = 0.5 \times 200 \times 0.0025 = 0.25 \text{ J}$$