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.