Kinetic Energy

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  • Kinetic energy is the energy possesed by the body by virtue of its motion
  • Body moving with greater velocity would posses greater K.E in comparison of the body moving with slower velocity
  • Consider a body of mass m moving under the influenece of constant force F.From newton's second law of motion
    F=ma
    Where a is the acceleration of the body
  • If due to this acceleration a,velocity of the body increases from v1 to v2 during the displacement d then from equation of motion with constant acceleration we have
    v22 -v12=2ad or
    a=v22 -v12/2d Using this acceleration in Newton's second law of motion
    we have
    F=m(v22 -v12)/2d
    or
    Fd=m(v22 -v12)/2
    or
    Fd=mv22/2 -mv12/2           (7)
    We know that Fd is the workdone by the force F in moving body through distance d
  • In equation(7),quantity on the right hand side mv2/2 is called the kinetic energy of the body
    Thus
    K=mv2/2
  • Finally we can define KE of the body as one half of the product of mass of the body and the square of its speed
  • Thus we see that quantity (mv2/2) arises purely becuase of the motion of the body
  • In equation 7 quantity
    K2=mv22/2
    is the final KE of the body and
    K1=mv12/2
    is the initial KE of the body .Thus equation 7 becomes
    W=K2-K1=ΔK           (9)
  • Where ΔK is the change in KE.Hence from equation (9) ,we see that workdone by a force on a body is equal to the change in kinetic energy of the body
  • Kinetic energy like work is a scalar quantity
  • Unit of KE is same as that of work i.e Joule
  • If there are number of forces acting on a body then we can find the resultant force ,which is the vector sum of all the forces and then find the workdone on the body
  • Again equation (9) is a generalized result relating change in KE of the object and the net workdone on it.This equation can be summerized as
    Kf=Ki+W           (10)
    which says that kinetic energy after net workdone is equal to the KE before net work plus network done.Above statement is also known as work-kinetic energy theorem of particles
  • Work energy theorem holds for both positive and negative workdone.if the workdone is positive then final KE increases by amount of the work and if workdone is negative then final KE decreases by the amount of workdone

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