# Energy , Finding Kinetic energy and Potential energy of an object

# Energy

**It is the ability to do work , Man needs the energy to exert effort ( do work ) without energy no task can be performed , The unit of measuring energy is the Joule ( J ) which is the same as the unit of measuring work , Energy has different forms such as Kinetic energy ( K E ) and potential energy ( P E ) .**

## Kinetic energy ( K E )

** Kinetic energy is the energy possessed by the object due to its motion , When work is done to move an object , this work is acquired by the object as kinetic energy , The unit of measuring the kinetic energy is Joule ( J ) and its dimensions are ML²T ^{−2} .**

**When the kinetic energy of an object is 400 J , It means that the energy possessed by the object due to its motion = 400 J . **

**Finding the kinetic energy of an object**

**If a force ( F ) acts on an object of mass ( m ) at rest to move it at a uniform acceleration ( a ) to reach velocity ( v _{f} ) after moving a displacement ( d ) . **

**Thus , v _{f}² = v_{i}² + 2 a d _{
}**

** v _{i} =0 ∴ v_{f}² = 2 a d , d = v_{f}² / 2 a**

**Multiplying both sides by the force ( F ) **

**∴ F d = ½ × v _{f}² × ( F / a )**

**From Newton’s Second Law :**

**F / a = m ∴ F d = ½ m v _{f}² **

**In the previous relation :**

**The left hand side ( F d ) represents the work done ( or the energy needed to move the object ) .
**

**The right hand side ( ½ m v _{f}² ) represents the form of energy into which work is converted which is the kinetic energy ( K E ) .
**

** KE = ½ m v²**

**Kinetic energy is a scalar quantity because it is the product of two scalar quantities which are mass and speed squared .
**

### Factors that affect kinetic energy of an object :

**The object mass ( m ) : Kinetic energy is directly proportional to the object mass at constant speed .**

**Slope = KE / m =½ v²**

**The object speed ( v ) : Kinetic energy is directly proportional to square speed of the object at constant mass .**

**Slope = KE / v² = ½ m**

**KE = ½ m v²**

**On applying the brakes to stop a car moving at velocity 30 km/h , the car would slide for a distance ( d ) before stopping .**

**The same car would slide for a distance four times longer on applying the brakes to stop it , if the car was moving at velocity 60 km/h , F d ∝ v² .**

** Potential energy ( P E )**

**It is the energy stored in the objects because of their new positions or state , When an object is lifted up , work is done , This work is stored in the body as energy known as gravitational potential energy , The unit of measuring the potential energy is the Joule ( J ) and its dimensions are ML²T ^{−2} .**

**When the potential energy of an object is 50 J , It means that the energy stored in the object because of its new position or state = 50 J .**

### Finding the potential energy of an object

**If an object of mass ( m ) is lifted up to a height ( h ) , the work done ( W ) is determined by the relation : W = F . h , Where ( F ) is the force required to lift the object up and equals its weight ( w ) : **

**F = w = m g ∴ W = m g h**

**The work done is stored in the form of potential energy ( P E ) .**

**P E** = **m g h**

**Factors that affect potential energy of an object**

**The object mass ( m ) : potential energy is directly proportional to the object mass at constant height and free fall acceleration , Slope = P E / m = g h .**

**The object height ( h ) : Potential energy is directly proportional to the object height at constant mass and free fall acceleration , Slope = PE / h = m g = w .**

**The free fall acceleration ( g ) : Potential energy is directly proportional to the free fall acceleration at constant object mass and height , Slope = P E / g = m h .**

## Examples of potential energy

**Stored energy in a spring when compressed or elongated ( elastic potential energy ) , The spring does work to release this energy and restore its original position .**

**Stored energy in an object when raised up above the ground ( gravitational potential energy ) , gravitational potential energy depends on the object position relative to the surface of the Earth .**

**Stored energy in a stretched rubber band ( elastic potential energy ) , The stretched rubber band shrinks when removing the acting force to restore its original shape .**

**Stored energy in electrons inside a battery ( electric potential ) , Electrons flow when the battery is connected to a closed circuit .**

## Notes

**To lift a box of weight 450 N vertically to a height of 1 m , We need a force equal to the box weight , The work done : W = 450 N × 1 m = 450 J**

**When raising the same box using a ramp ( inclined plane ) 3 m long , A force less than its weight is required ( 150 N ) but for a longer displacement , The work done : W = 150 N × 3 m = 450 J .**

**The sum of Kinetic energy and Potential energy is called Mechanical Energy .**

**Mechanical Energy** = **Kinetic energy + Potential energy**

**ME = KE + PE**

## Physics for the environment

**Most of the energy used by man comes from non-renewable resources such as Coal , Petroleum .**

**Non-renewable resources of energy are considered as unclean resources since they produce a lot of harmful products to the environment and man health . **

**Because of this , there is a global trend , especially in the most industrialized countries , to used the renewable resources such as wind power and waterfalls as an energy resource to generate electricity and preserve the environment , as well .**

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