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State and prove work Energy principle.
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Statement of Work-energy principle:

  • Change in Kinetic energy of the particle is equal to the total work done by number of forces in moving a particle through a displacement 's'.

Work done=Change in Kinetic Energy.

  • Work energy principle gives us a a relation between force, mass, velocity and displacement.

Proof:

  • Consider a particle of mass 'm' at the Orgin O of Cartesian system. Let force 'F' move the particle from O to A making a displacement of OA=x. Let 'u and ''v' be the velocity of particle at point O and point A respectively.
  • Force acting in the direction of displacement=F cos θ
  • By Newton's II law of motion,F=m a

Hence,Fcosθ=mdvdt

Hence,Fcosθ=mdvdx×dxdt

Thus, Fcosθ=m.dvdx×v

Hence, Fcosθ dx=mv dv

  • Integrating we get,

x0Fcosθ dx=vumv dv

F cosθ[x]x0=m[v22]vu

F cosθ [x0]=12m[v2u2]

F cosθ. x=12mv212mu2

  • Hence, Work done = Change in K.E, Thus Work-Energy principle is proved.
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