**Energy** is the ability or capacity to do work. Its unit is Joules.

**Types of Energy**

## Kinetic and Potential Energy Slides:

https://www.slideshare.net/slideshow/embed_code/key/vkZi6z5IFLEg7L**Potential and potential_energy for stoplearn.com**

Energy exists in various forms some of which are;

**Mechanical Energy**

Kinetic energy and potential energy constitutes mechanical energy. Kinetic energy is the energy a body possesses as a result of its motion. Potential energy on the other hand, is the energy possessed by a body because of its position. A body can also possess potential energy as a result of its nature. For example, an elastic material when stretched stores up energy (potential energy) which is given as ½ k e^{2} where k is what we call the elastic constant and e is extension in metres. Another form of potential energy is chemical potential energy which is energy stored up in a substance because of its chemical composition. Examples are; energy in the food we eat, electrolytes in cells or batteries.

Mathematically, Kinetic energy K.E=12(mv2).

M is mass in kilogram, v is velocity in m/s.

### Examples of bodies that possess kinetic energy are

- A rolling ball
- An object falling under gravity
- wind or air in motion
- An athlete running a race
- A bullet movement
- A plane flying.

If a body is raised to a height h, its potential energy is given as

P.E = mgh. Where m is mass in kilogram, h is height in metres and g is acceleration due to gravity.

**EVALUATION**

- Differentiate between potential energy and kinetic energy
- What is the formula for calculating kinetic energy and potential energy

**The Law of Conservation of Energy**

Energy as we have treated earlier exists in various forms. Although energy can be converted from one form to the other, the total energy remains conserved.

This is the law of conservation of energy. It states that energy can neither be created nor destroyed but can be converted from one form to the other.This law can be illustrated by mechanical systems as shown in the figures below.

**Energy Changes in a Simple Pendulum **

**For fig 1**

- As the pendulum bob approaches A, the velocityreduces until it becomes zero at point A where it momentarily comes to rest; thereby making the KE zero.
- Also at A, the bob attains its maximum height above the ground; thereby making the PE to be maximum.
- as the bob returns towards B, the velocity increases and the height decreases such that at B, velocity is maximum (since K.E=12(mv2), KE is also maximum).
- At B, height is zero, PE is equal to zero.
- At the middle point either between A and B or B and C, energy is conserved. Hence, PE =KE

**In fig. 2**, as the body moves from the horizontal ground C to A, its velocity reduces and at point A, at height h, where the body is stationary, the velocity v is zero. Consequently its kinetic energy is zero but the potential energy is maximum. As the body drops to the ground, its velocity increases and the vertical height h reduces to zero. Therefore, potential energy just before it touches the ground is zero and the body has maximum kinetic energy. At point B, the body possesses both Kinetic energy and potential energy. From the two illustrations we see that although the energy changes from kinetic to potential energy and vice versa, the total energy of the system is conserved or remains unchanged.

Another example where it is applied is for a falling body.

**Example 1**

A ball of mass 8kg falls from rest from a height of 100m. Neglecting air resistance, calculate its kinetic energy after falling a distance of 30m. (take g as 10m/s^{2}).

**Solution**

Initial velocity at height 100m, u = 0

Distance moved, s = 30m

a = 10ms^{-2}

Velocity after falling 30m, v = ?

v2=u2+2asv2=02+2×10×30v=6–√00v=24.5m/sK.E=12mv2=12×8×600K.E=2400J

Alternative solution:

*K.E = potential energy loss*

*= mgΔh*

K.E=8×10×30=2400J

**Example 2**

A body of mass 100kg is released from a height of 200m. With what energy does the body strike the ground? (g = 10 m/s^{2})

**Solution**

Gravitational potential energy is given as P.E=mgh=100×10×200=200,000

**Example 3**

A stone of mass 50.0kg is moving with a velocity of 20 m/s. Calculate the kinetic energy

**Solution**

mass = 50.0kg, velocity = 20 m/s

K.E=12mv2=12×50.0×20.0=500J

**EVALUATION**

- List eight forms of energy you know.
- State the law of conservation of energy and apply it to any mechanical system
- State the principle of conservation of energy. Using this principle explain how energy is conserved for (i) objects falling under gravity (ii) swinging of a simple pendulum bob.
- A ball of mass 1kg is dropped from a height of 5m and bounces to a height of 10m. Calculate (i) its kinetic energy just before impact. (ii) its initial bouncing velocity and kinetic energy.

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