Question

Derivation of work energy theorem

Full explanation step by step pls

Answer 1

Answer:

The work-energy theorem also known as the principle of work and kinetic energy states that the total work done by the sum of all the forces acting on a particle is equal to the change in the kinetic energy of that particle. ...

Explanation:

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Answer 2

Answer:The derivation of the work-energy theorem is provided here. The work-energy theorem also known as the principle of work and kinetic energy states that the total work done by the sum of all the forces acting on a particle is equal to the change in the kinetic energy of that particle.

Explanation:The work ‘W’ done by the net force on a particle is equal to the change in the particle’s kinetic energy (KE).

d=v(final)^2 - v(initial)^2/2a

Derivation Of Work Energy Theorem:-

Let us consider a case where the resultant force ‘F’ is constant in both direction and magnitude and is parallel to the velocity of the particle. The particle is moving with constant acceleration along a straight line. The relationship between the acceleration and the net force is given by the equation “F = ma” (Newton’s second law of motion), and the particle’s displacement ‘d’, can be determined from the equation:

v(final)^2 - v(initial)^2 = 2ad

Obtaining,

W= 'delta'KE =v(final)^2 - v(initial)^2/2a

The work of the net force is calculated as the product of its magnitude (F=ma) and the particle’s displacement. Substituting the above equations yields:

W =Fd = ma v(final)^2 - v(initial)^2/2a = v(final)^2 - v(initial)^2/2a = KE(final) - KE(initial) = 'delta'KE