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CBSE Class 12-science Answered

Define and deduce the following expression: (i) Kinetic Energy (ii) Work energy Theorem
Asked by nitika258369 | 11 Nov, 2020, 09:28: AM
answered-by-expert Expert Answer
If an object of mass m is moving with speed v ,  then kinetic energy KE is defined as
 
KE = (1/2)mv2 
 
--------------------------------------
 
Work-Energy Theorem
 
The change in kinetic energy of a particle is equal to the work done on it by the net force.
 
W e have the following relation for rectilinear motion underconstant acceleration a as
 
v2 − u2 = 2 ×a×S
 
where u and v are the initial and final speeds and S the distance traversed.
Multiplying bothsides by m/2, we have
 
(1/2)mv2 − (1/2)mu2 = m×a×S = F × S = W  ...........................(1)
 
where the last step follows from Newton’s Second Law i.e. product of mass and acceleration is force acting on the mass.
 
The left side of the equation is the difference in final kinetic energy and initial kinetic energy.
 The right side is a product of the displacement and the component of the force along the displacement, which is  workdone on the object and is denoted by W.
 
Eqn.(1) is then written as ,   Kf − Ki = W  .....................(2)
 
where Ki and Kf are respectively the initial and final kinetic energies of the object.
Work refers to the force and the displacement over which it acts and Work is done by a force on the body over a certain displacement.
 
Equation (2) is the mathematical statement of Work-energy theorem
Answered by Thiyagarajan K | 11 Nov, 2020, 04:42: PM
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