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 .
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 :
- An increase in the potential energy of the object with height .
- 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
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 .