Kinetic energy

Kinetic energy is the energy that an object possesses due to its motion. To calculate the kinetic energy of an object, use the formula:

${\text{E}}_{\text{k}}=\frac{1}{2}{\text{m v}}^2$

Where:

E_k = kinetic energy (J)

m = mass (kg)

v = speed (m s^-1)

Worked example - Kinetic energy of a rolling ball

Calculate the kinetic energy of a ball rolling with a velocity of 5 m s^-1^ and a mass of 2 kg.

Step 1: Formula

${\text{E}}_{\text{k}}=\frac{1}{2}{\text{ m v}}^2$

Step 2: Substitution and correct evaluation

${\text{E}}_{\text{k}}=\frac{1}{2}\times 2\times 5^2=\frac{1}{2}\times 2\times 25=25\text{ J}$

Gravitational potential energy

Gravitational potential energy is the energy stored in an object as a result of its vertical position within a gravitational field.

It is calculated using the formula:

${\text{E}}_{\text{p}}\text{ = m g h}$

Where:

• m = mass (kg)
• g = acceleration due to gravity (9.81 m s^-2^).
• h = height above reference point (m).

Worked example - Gravitational potential energy of a raised ball

Let's calculate the gravitational potential energy of a ball that weighs 1 kg and is raised to a height of 10 meters.

Step 1: Formula

${\text{E}}_{\text{p}}\text{ = m g h}$

Step 2: Substitution and correct evaluation

${\text{E}}_{\text{p}}=1\times 9.81\times 10=98.1\text{ J}$

Conservation of mechanical energy

The law of conservation of energy states that energy is only transformed from one type to another; it is neither created nor destroyed.

In the case of a pendulum, the total mechanical energy is maintained throughout its motion. As it swings, the pendulum's energy constantly transforms between kinetic energy and potential energy.

Key points:

• At the highest points of its swing, the pendulum has maximum potential energy and minimum kinetic energy.
• At the lowest point of its swing, the pendulum has maximum kinetic energy and minimum potential energy.