Work-Energy Theorem | Physics Grade XI

Theorem

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Work-Energy Theorem | Physics Grade XI

Work-Energy Theorem

Work-Energy Theorem

Statement: Total work done by a force acting on a body is the total change in its kinetic energy.

Proof: Suppose a body of mass m is moving on a smooth horizontal surface with a constant velocity, u. Let a constant force F acts on the body from point A to B as shown in the figure such that the velocity increases to v. The work done by the force is

  W = F s

Where 's' is the displacement of the body.

Displacement of body

From Newton’s second law of motion,
F =ma
 Then, work done is given by
W = ma s
Let the initial kinetic energy be K.E1 = ½mu2 and final kinetic energy be K.E2 = ½mv2,
Then,
From the equation of motion v2 = u2 + 2as,
v2 – u2 = 2as
or, as = ½ (v2 – u2)
since, W = mas = m. ½ (v2 – u2)
= ½mv2 –½mu2
= K.E2 – K.E1
So, the work done on moving the body from A to B by applying force F is equal to the increase in Kinetic energy of the body. Again, we can write the above equation as,
W = ½mv2 –½mu2
½mv2 = W +½mu2
That is, the final kinetic energy of the body is increased and it is the sum of the work done by the body and its initial kinetic energy.

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