Question

Prove work-energy theorem for a constat force

Answer 1

Let us consider an object of mass m which is moving under the influence of constant force F. From Newton’s second law of motion:

F = ma

Where,

a = acceleration of the object

The velocity of the object increases from v1 to v2 due to the acceleration, and the object displaces by a distance d.

v22−v12=2ad, or

a = (v22−v12)/2d, or

Now we have,

F = m (v22−v12)/2d, or

Fd = m (v22−v12)/2d, or

Fd = ½ m.v22 – ½ m v12 -------(i)

Fd is the work done by the force F to move the object through a distance d.

In equation (i), the quantity

K2 = m.v22/2, is the final Kinetic energy of the object, and the quantity

K1=mv12/2

Is the initial Kinetic of the object

Thus equation (i) becomes

W=K2-K1=ΔK------(ii)

Where,

ΔK = change in KE of the object.

From equation (ii), it is clear that the work done by a force on an object is equal to the change in kinetic energy of the object.

Answer 2

Answer: work energy theorem for constant force

Explanation:

According to this theorm the change in kinetic energy of an object is equal to the work done by the object

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