Question

State law of conservation of energy. Derive the equation for a freely falling body?

Answer 1

the sum of kinetic and potential energy of an object is called its total mechanical energy it is considered a body of mass M placed at a as shown in the figure
let H = ab = height of the body above the ground
S be the distance of any point from a
V1=velocity of the body at C
and V is a velocity of body at b
object just above the ground s minus is the distance between C and b
the velocity at the point A is zero
that is u is equal to zero
1. at point a
potential energy =MGH
and kinetic energy =zero
total mechanical energy is equal to potential energy + kinetic energy
= MGH mark this is a equation 1
2.at point c
similarly when the body moves from a to c it covers a distance s
if V1 is the velocity at C then
from V1 square - U square = 2 GS
potential energy =MG(H-s)
kinetic energy = MGS
mechanical energy = kinetic energy + potential energy
= MGH - MGS + MGS
=MGH mark this is equation 2 3.at. B
v ^2 - u square = 2 GH
v square =2 GH
potential energy = 0
Kinetic energy = MGH
mechanical energy = kinetic energy + potential energy
=0 + MGH
= MGH mark this as equation 3

AS the mechanical energy at point A= the mechanical energy at point c =mechanical energy at point B

as mechanical energy is equal at every point in the situation of free falling this states that

energy can neither be created nor be destroyed which is the law of conservation of energy
and with this the proving of conservation of energy done

Answer 2

Refer the attachment ❤️