 # Work and Kinetic Energy

We all have heard the stories of great explorers who sailed the unknown seas in their sailboats.  Those were the days before any engine was in existence.  They only relied on wind to move their huge ships. How does the wind move such objects? The answer lies in the principles of Kinetic energy.  In this article, we shall understand its basic principles and how can it equate to work.

### Suggested Videos         ## Kinetic Energy Definition

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. The kinetic energy of an object is denoted by KE and its SI unit is joules (J). By now, we have started to sense that work and kinetic energy are closely related.  But, are they interchangeable? Can work be expressed in terms of the kinetic energy of an object and vice versa? Let us see!

### Work and Kinetic Energy – The Work-Energy Theorem

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.

#### Solved Examples For You

Q 1: Which of the following kind of energy depends upon the mass and the square of the speed of a body?

A) Kinetic     B) Potential     C) Electrostatic     D) Nuclear

Solution: A) The Gravitational Potential energy, Nuclear and Kinetic Energy all depend on mass. But out of the three only Kinetic energy is such that it contains the term with the square of velocity. So the answer is A.

Q 2: A rigid body of mass m kg is lifted uniformly by a man to a height of one metre in 30 sec. Another man lifts the same mass to the same height in 60 sec. The work done on the body against gravitation in both the cases are in the ratio:

A) 1:2     B) 1:1     C) 2:1    D)    4:1

Solution: B) Well whoever said anything about work depending on time, right? Work is independent of time as W = F.s doesn’t contain time (as long as the force is time independent!). So we can say that in this case, the work done will be similar in both cases and will present a ratio of 1:1.

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