State law of conservation of energy mathamatically

urgent!!

Law of conservation of energy:-

m = mass of body

g = Acceleration due to gravity

Suppose a body is at point A initially. Then it falls freely, during the motion mechanical energy of the body is conserve.

At point A,

AC = height of object from ground

= h

Initial speed u = 0

So, P.E. = mgh

TE = P.E + K.E = mgh + 0

(TE)_A = mgh ... (i)

At point B,

PE = mg (BC)

= mg (h – x) = mgh – mgx

Use kinematics equation

(TE)_B = P.E. + K.E = mgh – mgx + mgx

= mgh ...(ii)

At point C,

P.E. = 0

Use kinematics equation

⇒ v ² = 2gh

So,

(T.E.)_C = K.E + P.E. = mgh +0 = mgh ...(iii)

(TE)_A =(TE)_B=(TE)_C

Hence, the total energy of the body is conserve during free fall.