Question

State and prove the law of conservation of energy in the case of a freely falling object.

Answer 1

⏹Let's consider a case....

✔️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

K.E=1/2mv2

=1/2m(0)

=0

➖TE = P.E + K.E = mgh + 0

⏹TE= total energy

⏹PE=potential energy

⏹KE= kinetic energy

✔️(TE)A = mgh .................................... (i)

✔️⏹✔️At point B,

PE = mg (BC)

= mg (h – x) = mgh – mgx

Use kinematics equation......

⏹ Refer attachment for formula ⏹

✔️(TE)B = P.E. + K.E = mgh – mgx + mgx

= mgh ...(ii)

✔⏹️✔️At point C

P.E. = 0

KE=1/2mv2

✔️Now use kinematic equation again...
v2=u2+2gh

 v 2 = 2gh

So, 

➖Substitute the value again...
KE=1/2m(2gh)

=mgh

✔️(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..........