Prove that the increase in kinetic energy of a body=work done by the force on the body.The velocity of the body is increased by applying a constant force for some distance in the direction of motion.
Asked by aahnik.mohanty | 19th Dec, 2017, 09:13: PM
Expert Answer:
(Note :- Vectors are typed as Bold letters)
Workdone = Force × distance = F • d
Force F = Rate of change of momentum = m(vf - vi)/t
m - mass of object, vf and vi are final and initial velocity respectively. t is time taken for the velocity change.
distance travelled in time t = t × (vf+vi)/2
Hence workdone = [ m(vf - vi)/t ] • [t × (vf + vi)/2 ] = (1/2)×m× (vf-vi) • (vf+vi) = (1/2)×m×(vf2 - vi2) = change in kinetic energy
Answered by | 20th Dec, 2017, 11:13: AM
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