Question

Why is kinetic energy and work equal?

Answer 1

energy which possess motion is called kinetic energy. Ex. an athletes running in Olympics

Answer 2

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Kinetic Energy of an object is its capacity to put another object in motion. A force displacing an object does work. Also, we know that when an object in motion strikes a stationary object, it can cause it to move. Hence it can do work. Thus, we define the kinetic energy as the capacity of an object to do work by virtue of its motion.



Consider an object with an initial velocity ‘u’. A force F, applied on it displaces it through ‘s’, and accelerates it, changing its velocity to ‘v’. Its equation of motion can be written as: v2 – u2 = 2as

Multiplying this equation by ‘m’ and dividing throughout by 2, we get:

mv2/2 – mu2/2 = mas; where ‘m’ is the mass of the object.

Hence, mv2/2 – mu2/2 = Fs; where F is the force that caused the havoc!

Therefore, we can write mv2/2 – mu2/2 = W; where W = Fs is the work done by this force.

So what just happened? We just proved that 1/2 (mv2) – 1/2 (mu2) is the work done by the force! In other words, the work done is equal to the change in K.E. of the object! This is the Work-Energy theorem or the relation between Kinetic energy and Work done. In other words, the work done on an object is the change in its kinetic energy.  W = Δ(K.E.)

The engine of your motorcycle works under this principle. The explosion of the burning mixture of fuel and air moves the piston. The moving piston, in turn, moves the crank of the engine, which, in turn, moves the selected gear and hence the drive chain that rotates the driving wheel of the motorcycle.

Therefore, engineers use the work-energy theorem to calculate the work done by each progressive component of the engine in its chain of motion. By calculating the difference in work done, engineers can isolate the performance of each component of the drivetrain and attempt to improve its efficiency.



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