# Introduction to Energy, conservational law, Mechanical energy; potential and kinetic energy, examples

Energy can be defined as the capacity to perform work. Thus, the unit of energy is the same as that of work. That is, the s.i unit of energy is joule. We have various types of energy; kinetic energy (Such as, the energy from a moving car or a falling stone), chemical energy, heat energy, electrical energy,  light energy, light energy, sound energy, nuclear energy.

Conservation law

All the forms of energy listed above can be changed from on form to another by means of suitable machine or apparatus, for example; the energy in the nucleus of atoms produces heat energy, which in turn can be used to generate electrical energy. The mechanical energy that moves a car comes from heat  energy derived from the volume of fuel which is stored as chemical energy.

The principle of conservation of energy states that although energy can be changed from form to another, the total energy of given system remains unchanged i.e energy can neither be created nor destroyed during transformation.

Mechanical Energy

A body can possess mechanical energy or have the ability to work for two reasons either by virtue of its position or because of its motion. The two kinds of energy are called kinetic energy and potential energy respectively.

Kinetic energy
It is energy a body possesses because it is in motion.
Mathematical formula,
KE =   1/2 mv2       Where m = mass, v = velocity.

Potential energy
It is the energy a body possesses because of its position. A body of mass (m) raising to a height (h) above the ground is said to possess potential energy.
Mathematical formula,
KE = mgh       Where m = mass, g = acceleration due to gravity, h = distance.

Power: This is defined as the rate of doing work or the rate of transfer of energy.
Average power = (work done or energy extended)/(time taken)
Power = (mgh)/t
The S.I unit of power is watt (W),former unit of power was horse-power.

Examples

1) A boy of mass 30kg is running with a speed of 4 m/s. What is his kinetic energy?
Solution
KE =   1/2mv2
M = 30kg, v = 4m/s
KE = 240J

2) A bullet of mass 4g is moving with a speed of 216 km/hr. Calculate its kinetic energy.

Solution

M = 0.04 kg
V = 216km/hr
1hr = 60min
1000m = 1km
V =  60m/s
KE =72J

3)  Calculate the power of a pump which lifts 500kg of water through a vertical height of 4m in 5 seconds.

Solution

P = mgh/t
m = 500kg
h=4m
g=10m/S2
Power = 4000J

4) A bullet of mass 0.05kg has a speed of 400m/s. What is the kinetic energy, if it hits a wall of which of the average resistance is 10000N. Calculate the distance penetrated by the bullet.

Solution

KE =   1/2mv2
KE = 0.5 x 0.05 x 400 x 400
KE = 4000J
Energy =work done = Force x distance
4000J = 10000 x d
Distance penetrated by the bullet = 0.4m