Question

state and prove work energy therom​

Answer 1

Work energy theorem states that the change in kinetic energy of an object

is equal to the net-work done on it by the net force.

Let us suppose that a body is initially at rest and a force.

F

is applied on the body to displace it through

d

s

along the direction of the force. Then, a small amount of work done is given by

dw =

F

.d

s

= Fds

Also, according to Newton's second law of motion, we have

F = ma

where a is acceleration produced (in the direction of force) on applying the force. Therefore,

dw = Mada = M

dt

dv

ds

Now, work done by the force in order to increase its velocity from u (initial velocity) to v (final velocity) is given by

W = ∫

u

v

Mvdv = M∫

u

v

vdv

= M∣

2

v

2

∣

u

v

W =

2

1

Mv

2

−

2

1

Mu

2

Hence, work done on a body by a force is equal to the change in its kinetic energy.

Answer 2

Answer:

The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. ...

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