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State and explain work energy theorem |
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Answer» Work energy theorem states that the change in kinetic energy of an object is equal to the net work done on it by the net force. Let us suppose that a body is initially at rest and a force \(\vec{F}\) is applied on the body to displace it through \(d\vec{S}\)along the direction of the force. Then, small amount of work done is given by dW = \(\vec{F}\).\(d\vec{s}\) = FdS Also, according to Newton's second law of motion, we have F = ma where a is acceleration produced (in the direction of force) on applying the force. Therefore, dW = MadS = M\(\frac{dv}{dt}\)dS OR dW = M\(\frac{dS}{dt}\)dv = Mvdv Now, work done by the force in order to increase its velocity from u (initial velocity) to v (final velocity) is given by W = \(\int^v_uMvdv\) = M\(\int^v_uvdv\) = M\(\Big|\frac{v^2}{2}\Big|^v_u\) W = \(\frac{1}{2}Mv^2-\frac{1}{2}Mu^2\) Hence, work done on a body by a force is equal to the change in its kinetic energy. |
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