# Law of Conservation of mechanical Energy in everyday life

The energy is the capacity to do work , There are different forms of energy that can be converted into one another , Such as in the waterfall , The potential energy is converted into kinetic energy , The electrical energy is converted in the electric bulb into heat and light energies .

Chemical energy stored in coal , gasoline and other types of fuel is converted on burning into heat energy then mechanical work that is used by means of transportation such as cars and trains .

On converting energy from one form into another , the amount of energy remains constant , This is known as the law of conservation of energy .

Law of conservation of energy : Energy is neither created nor destroyed , but it can be converted from one form into another .

Law of conservation of energy

#### Law of conservation of mechanical energy

Assume that an object of mass ( m ) is projected vertically upwards from point ( 1 ) at initial velocity ( vi ) to reach point ( 2 ) at final velocity (vf) , the work done on the object while rising leads to :

1. An increase in the potential energy of the object with height .
2. A decrease in the kinetic energy of the object due to a decrease in its velocity .

According to the third equation of motion : vf² − vi² = 2 a d

Since the object moves upwards against gravity , it decelerates uniformly .

a =− g      ∴  vf² − vi² = 2 (− g ) d    multiply ( ½ m )

½ m ( vf² − vi² ) = − m g d   ,  d = yf − yi

½ m ( vf² − vi² ) = − m g ( yf − yi )

½ m vf² − ½ m vi² = − m g yf + m g yi

m g yf + ½ m vf² =  m g yi + ½ m vi²

PEf + KEf = PEi + KEi

This means that : The sum of potential energy and kinetic energy at point ( 1 ) = The sum of potential energy and kinetic energy at point ( 2 ) .

The sum of potential energy and kinetic energy of an object at any point on its path under the effect of gravity only = constant .

The increase in the kinetic energy of a falling object will be on the expense of its potential energy , potential energy decreases and vice versa .

The mechanical energy : It is the sum of potential energy and kinetic energy of an object , Mechanical energy ( M E ) = P E + K E .

Law of conservation of mechanical energy : The sum of potential energy and kinetic energy of an object at any point on its path under the effect of gravity only is constant .

##### Law of conservation of energy in everyday life

There are many examples of mutual transformation between potential energy and kinetic energy , like :

The roller coaster acquires the maximum potential energy at the top which is then converted into kinetic energy on falling .

When flinging arrows , potential energy is stored in the string and bow and then converted into kinetic energy when the string is released .

In pole vault , potential energy is stored in the pole and then converted into kinetic energy .

Projecting an object upwards : When a ball is thrown from the ground upwards , potential energy of the ball is zero at the ground , while kinetic energy is maximum .

As the ball rises , its potential energy increases and its kinetic energy decreases , Potential energy reaches its maximum value at the height point reached by the ball where its kinetic energy = zero .

When the ball starts to fall to the ground , its kinetic energy increases gradually , while its potential energy decreases .

When the ball reaches the ground , the potential energy becomes zero at the ground while kinetic energy becomes maximum .