State and prove the work-energy theorem. OR Show that work done by a

1.	State and prove the work-energy theorem. OR Show that work done by a moving body is equal to the change in K.E. of the body.
Answer» The work energy theorem states that work done on a body is equal to the net change in its energy. (P.E or K.E) Proof: Consider a body of mass ‘m’ moving with an initial velocity u. Let a constant force F acting on a body changes its velocity to v. Let s be the distance traveled. From the equation, v² = u² + 2as, we get v² – u² = 2as \(\frac {1}{2}\)(v² – u²) = as Multiplying both sides by m,we have \(\frac {1}{2}\)m(v² – u²) = mas \(\frac {1}{2}\)m(v² – u²) = F.s (∵ F = ma) or \(\frac {1}{2}\)mv² – \(\frac {1}{2}\)mu² = W.

State and prove the work-energy theorem. OR Show that work done by a moving body is equal to the change in K.E. of the body.

Answer»

The work energy theorem states that work done on a body is equal to the net change in its energy. (P.E or K.E)

Proof:

Consider a body of mass ‘m’ moving with an initial velocity u. Let a constant force F acting on a body changes its velocity to v. Let s be the distance traveled.

From the equation, v² = u² + 2as,

we get v² – u² = 2as

\(\frac {1}{2}\)(v² – u²) = as

Multiplying both sides by m,we have

\(\frac {1}{2}\)m(v² – u²) = mas

\(\frac {1}{2}\)m(v² – u²) = F.s

(∵ F = ma)

or \(\frac {1}{2}\)mv² – \(\frac {1}{2}\)mu² = W.

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