Conservation Of Mechanical Energy In A Freely Falling Body

Let a body of mass m lying at position A at a height h above the ground. As the body falls, its Kinetic Energy increases at the expense of potential energy.

Conservation Of Mechanical Energy In A Freely Falling Body
Conservation Of Mechanical Energy In A Freely Falling Body
At Point A

The body is at rest

Conservation Of Mechanical Energy In A Freely Falling Body
Conservation Of Mechanical Energy In A Freely Falling Body
At Point B

Let the body falls freely through height x and reaches the point B with velocity v, then

Conservation Of Mechanical Energy In A Freely Falling Body
Conservation Of Mechanical Energy In A Freely Falling Body
At Point C

Let the body finally at point C on the ground with velocity v’, then considering Motion from A to C.

Conservation Of Mechanical Energy In A Freely Falling Body
Conservation Of Mechanical Energy In A Freely Falling Body

Clearly, As the body falls, Its Potential Energy decreases and Kinetic Energy increases by an equal amount. However the total Mechanical Energy remains constant at all points.

Given below are the graph represent the above situation.

Conservation Of Mechanical Energy In A Freely Falling Body
Conservation Of Mechanical Energy In A Freely Falling Body

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