# 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 mechanical energy**

**Assume that an object of mass ( m ) is projected vertically upwards from point ( 1 ) at initial velocity ( v _{i} ) to reach point ( 2 ) at final velocity (v_{f}) , 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 : v _{f}Â²Â âˆ’Â v_{i}Â²Â = 2 a d**

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

**a =âˆ’ gÂ Â Â Â Â âˆ´Â v _{f}Â²Â âˆ’Â v_{i}Â²Â = 2 (âˆ’ g ) dÂ Â Â multiply ( Â½ m ) **

**Â½ m ( v _{f}Â²Â âˆ’Â v_{i}Â² ) = âˆ’ m g dÂ Â ,Â d = y_{f} âˆ’ y_{i}**

**Â½ m ( v _{f}Â²Â âˆ’Â v_{i}Â² ) = âˆ’ m g ( y_{f} âˆ’ y_{i} )**

**Â½ m v _{f}Â²Â âˆ’ Â½ mÂ v_{i}Â² = âˆ’ m g y_{f} + m g y_{i}Â **

** m g y _{f}Â + Â½ m v_{f}Â² =Â m g y_{i} + Â½ mÂ v_{i}Â² **

**PE _{f} + KE_{f} = PE_{i} + KE_{i}**

**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 the 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, the 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.**

**Energy resources & forms, Potential energy, Kinetic energy & Mechanical energy**

**Potential energy, Kinetic energy & Law of conservation of mechanical energy**