state and prove work-energy principle
Answers
Work Energy principle states that, the change in kinetic energy of an object/body equals to the net work done on that object
Mathematically it can be expressed as
W = ΔK.E = (1/2)m(v₂ -v₁)
Here m= mass
v₂ and v₁ = final and initial velocity of the body.
Work energy principle makes use of the Newton's II nd law of motion, which states that force is the product mass and acceleration.
Mathematically,
F = ma ; a= acceleration
Also we know a = {Final (v₂) - Initial velocity (v₁)}/time (t)
Also from equation of motion we have,
v² = u² +2as
s = (v₂² - v₁²)/2a -----(A)
Now work done W = Force × displacement
W = ma × s
Putting the value of A in the above equation we get,
W = ma× (v₂² - v₁²)/2a
W = (1/2)m(v₂² - v₁²) ------(B)
We have Kinetic energy K.E = (1/2) m v²
Hence equation B can written as
W = K.E₂ - K.E₁ = ΔK.E
Answer:
work energy theorem State that the work done by net force acting on a body is equal to the change produced in the kinetic energy of the body.
we have,
v²= u²+2as
=>v²-u²=2as
=>1/2v²-1/2u²=as
=>1/2mv²-1/2mu²=mas
=>Kf-Ki=∆W
proved