Proof K.E = 1/2 m v2

by • 04/07/2012 • GeneralComments (0)558

Proof

Kinetic energy of a moving body is measured by the amount of work that a moving body can do against an unbalanced force before coming to rest.

Consider a body of mas ‘m’ thrown upward in the gravitational field with velocity v. It comes to rest after attaining height ‘h’. We are interested in finding ‘h’.

Therefore, we use

2 a S = vf2 – vi2 ………………………. (1)

Here a = -g

S = h = ?

vi = v (magnitude of v)

vf = 0

Therefore,

(1) => 2(-g) = (0)2 – (v)2

-2 g h = -v2

2 g h = v2

h = v2/2g

Therefore, Work done by the body due to its motion = F . d

= F d cos θ

Here

F = m g

d = h = v2 / 2g

θ = 0º

Therefore, Work done by the body due to its motion = (mg) (v2/2g) cos0º

= mg x v2 / 2g

= 1/2 m v2

And we know that this work done by the body due to its motion.

Therefore,

K.E = 1/2 m v2

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