CBSE Class 11-science Answered
state and prove worh-energy theorm
Asked by karamvirsingh79 | 20 Oct, 2019, 05:09: PM
Expert Answer
The change in kinetic energy of a particle is equal to the work done on it by the net force.
If a particle moving with initial speed u with acceleration a , then its final speed after travelling a distance S is given by,
v2 = u2 + ( 2 a S ) or v2 - u2 = 2 a S .................(1)
Multiplying both sides by (1/2)m, where m is mass of particle, we get,
(1/2)mv2 - (1/2)mu2 = m a S .................(2)
By newtons law, we have, F = ma ...............(3)
where F is the force acting on the particle that accelerates the particle.
using eqn.(3), eqn.(2) is written as, (1/2)mv2 - (1/2)mu2 = F × S .................(4)
Let us denote ‘half the mass times the square of the speed’ as kinetic energy K .
Hence LHS of eqn.(4) is difference of final and initial kineteic energies.
RHS of eqn.(4), i..e., product of force acting on the particle and distance moved by particle
while force is acting is known as work done W by the force.
Work refers to the force and the displacement over which it acts.
Then we write eqn.(4) as, Kf − Ki = W ........................(5)
where Ki and Kf are respectively the initial and final kinetic energies of the object.
Eqn.(5) is the mathematical statement of work-energy theorem
Answered by Thiyagarajan K | 20 Oct, 2019, 09:09: PM
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