# Calculate Law of Conservation of Energy - Tutorial

## Calculate Law of Conservation of Energy - Definition, Formula, Example

##### Definition:

The law of conservation of energy states that energy may neither be produced nor destroyed. Therefore the amount of all the energies in the system is a constant.

##### Formula:
Energy Conservation, At Point A
 Energy total = K.E. + P.E = 0 + mgh = mgh
At Point B
 Energy total = K.E. + P.E = mgh + 1/2mV2
To calculate v we make use of 3rd equation of motion, v2=u2+2gS
At Point C
 Energy total = K.E. + P.E = 0 + 1/2mV2
To calculate v we make use of 3rd equation of motion, v2=u2+2gS
Where, K.E = Kinetic Energy P.E = Potential Energy m = mass g = acceleration due to gravity, g = 9.8 m/s2 h = height ##### Example:

A stone of mass 10 gram is placed at the top of a tower 50 m high and it is allowed to fall freely. Find out the energy conservation at points A, B and C?

##### Given,

Mass of stone = 10g = 10/1000 kg = 0.001 kg. Acceleration due to gravity,g = 9.8 m/s2 Height = 50 m

##### To Find,

Energy Conservation At Point A,B,C

##### Solution :

Substitute the given values in the formula,

Energy Conservation At Point 'A'
 P.E at A = mgh = 0.01 x 9.8 x 50 = 0.01 x 98 x 5 = 4.9 J
 K.E at A = 1/2 mv2 =1/2 m * 0 (stone is at rest) = 0

Total energy at A = P.E + K.E= 4.9 + 0 = 4.9 J

Energy Conservation At Point 'B'

Height from the ground = 40 m

 P.E at B = mgh = 0.01 x 9.8 x 40 = 0.01 x 98 x 4 = 3.92 J

K.E at B = 1/2 mv2 To calculate v we make use of 3rd equation of motion

,v2=u2+2gS

u=0 (u is the initial velocity of a moving stone) v2=0+2*9.8*10 v2=196

 Therefore, K.E at B = 1/2 * 0.01 * 196 = 0.98

Total energy at B = P.E + K.E= 3.92 + 0.98 = 4.9 J

Energy Conservation At Point 'C'

Height from the ground = 0 m

 P.E at C = mgh = 0.01 x 9.8 x 0 =0 J

K.E at B = 1/2 mv2 To calculate v we make use of 3rd equation of motion,

v2=u2+2gS

u=0 (u is the initial velocity of a moving stone) v2=0+2*9.8*50 v2=980

 Therefore, K.E at C = 1/2 * 0.01 * 980 = 4.9

Total energy at C = P.E + K.E= 0 + 4.9 = 4.9 J The total energy at A, B and C is 4.9 J. This means the law of conservation of energy holds good in the case of an object falling freely under gravity.