**Energy **of a system is defined as its capacity to do work. (Note: Work is covered in the next sub-topic)

- SI unit : joules (J)
- Scalar Quantity; Energy has magnitude only.

## Principle of Conservation of Energy

The Principle of conservation of energy states that energy cannot be created nor destroyed in any process.

- Total amount of energy of a closed system remains
**constant.** - Energy can be converted/transformed from one form to another. (
**Note:**You can think of the different forms of energy as some form of “currencies”, whereby the exchange rates among the different “currencies” are 1:1.)**E.g. 1:**A television converts electrical energy(electricity) into light, sound and thermal energies.**E.g. 2:**Burning of fuels (wood) converts stored chemical energy into heat and light energies.

- It can also be transferred from one body to another through work done and/or heat exchanges.

## Forms of Energy

- Potential Energy (Elastic, gravitational and chemical)
- Kinetic Energy (or mechanical energy)
- Electrical Energy
- Thermal Energy (or heat)
- Light
- Nuclear Energy

### Kinetic Energy

**Kinetic Energy**, $E_{k}$ is the energy a body possessed by virtue of its motion.

- Moving objects have kinetic energy.
- Kinetic energy can be used to do work.

$$E_{k} = \frac{1}{2} m v^{2}$$

where m = Mass (in kg), v = Velocity (in $\text{m s}^{-1}$)

### Potential Energy

**Potential Energy** is the stored energy in a system.

- Example of chemical potential energy: Wood; When you burn wood, the chemical potential energy in wood is converted into thermal energy (heat) and light.
- Example of elastic potential energy: Rubber band; When you stretch a rubber band, elastic potential energy is stored in the stretched rubber band.

#### Gravitational Potential Energy

**Gravitational Potential Energy** is defined as the amount of work done in order to raise the body to the height *h* from a reference level.

$$G.P.E.= mgh$$

, where m = mass (in kg), g = acceleration due to gravity (in $\text{m s}^{-2}$), h = height (in m)

#### Conversion of Gravitational Potential Energy to Kinetic Energy & Vice Versa

An object at $X$ m above the reference level (commonly taken to be the ground level) will have gravitational potential energy of $mgX$. When the object is released from the height ($X$ m), the object will have all its gravitational potential energy gradually converted into kinetic energy, just before it hits the ground. (Assuming that there is no air resistance)

From the diagram above, the conversion of kinetic energy to gravitational potential energy, and back to kinetic energy is shown.

The next few sub-topics contain some case studies and worked examples. The case studies (oscillating pendulum and bouncing balls) and worked examples highlight the conversion of kinetic energy into gravitational potential energy and vice versa. They will help to solidify your understanding towards the concept.

## Self-Test Questions

### Consider a car moving at a speed of $v \text{ ms}^{-1}$. If the speed of the car slows down to $\frac{v}{2} \text{ ms}^{-1}$, how much will the kinetic energy of the car decrease by?

**Click here to show/hide answer**

Recall that kinetic energy is given by $\frac{1}{2} mv^{2}$.

We will use $E_{i}$ to denote the initial kinetic energy and $E_{f}$ to denote the final kinetic energy.

We have:

$$\begin{aligned} E_{i} &= \frac{1}{2} m v^{2} \\ E_{f} &= \frac{1}{2} m \left( \frac{v}{2} \right)^{2} \end{aligned}$$

Notice that $E_{f}$ can be simplified to:

$$\begin{aligned} E_{f} &= \frac{1}{4} \frac{1}{2} m v^{2} \\ &= \frac{1}{4} E_{i}\end{aligned}$$

The kinetic energy of the car will decrease by a factor of 4.

### A pendulum bob swings from one end to the other. At which point (s) will the gravitational potential energy of the pendulum be (a) maximum, (b) minimum?

**Click here to show/hide answer**

Recall that the gravitational potential energy is given by $E_{GPE} = mgh$.

a) The gravitational potential energy of the pendulum will be the highest (maximum) when it is at the maximum height. The pendulum bob is at the maximum height at the two extreme ends of the oscillation.

b) The gravitational potential energy of the pendulum will be the lowest (minimum) when it is at the minimum height. The pendulum bob is at the minimum height at the centre of the oscillation.

Great work

Adjust your way of writing the formulars

But no one is changing it, why?

I think there is an error here: “When the raised pendulum is released from A, it will swing towards the equilibrium position (Point B). During this movement, the gravitational potential energy is converted into kinetic energy. Hence, at A, gravitational potential energy is at minimum, while kinetic energy is at maximum.” The sentence- “Hence, at A,” should be hence at B,

Yes, there is an error…

Yes it is written wrong here

Fixed. Thanks!