Question

Develop the notions of work and kinetic energy and show that it leads to work energy theorem.

Answer 1

Notion of Work and kinetic energy : The work-energy theorem states that the change in kinetic energy of a particle is equal to the work done on it by the net force. e.g., mathematically, $K_f-K_i=W_{\textbf{net force}}$

We know the equation from 3rd kinematics equation of motion ,
v²  – u² = 2as
Where u is the initial velocity, v is the final velocity, a is the acceleration, and s is the displacement of particle

Now, v² - u² = 2as
Multiplying m both sides,
or, mv² - mu² = 2ams
or, 1/2mv² - 1/2 mu² = mas

From Newton's 2nd law, F = ma
and final kinetic energy , kf = 1/2mv²
initial kinetic energy , ki = 1/2mu²

Now, kf - ki =F.s = workdone
Hence proved that change in kinetic energy equals workdone by net force on it.

Answer 2

WORK : work done by a force is defined as the product of component of the direction of the displacement and magnitude of the displacement.

KINETIC THEORY: the energy possessed by a body by virtue of its motion is called as kinetic energy .

WORK ENERGY THEOREM : the work done on a particle by the net force is equal to the change in kinetic theory.

Let us consider a body of mass M and acceleration a with initial velocity Vi lets it’s uniform force be F : Vf square - Vi square = 2as. Multiplying both the equations by m/2 we get : 1/2 MVf square - 1/2 MV1 square =M/2[2as] =Mas = f.s •

The left side of the equation is the difference in the quality half the mass times the square of the speed front m it’s initial value to its final value . We call this as kinetic energy .

The right side is the product of the displacement

and the component of the force along the displacement . This quantity is called work then Kf- Ki =W