Work Done in Physics /Explanation of Work done

  

Today we will discuss what is Work Done In Physics? and I will give  examples of work done in daily life.  I will also show some figure which will help you to understand work done.

Work:-

Introduction:-

The Work is said to be done in physics when force causes displacement in body. Simply we can say that the product of the force along displacement and the magnitude of displacement.

Concept of Work in Physics:-

The concept of work in physics is much more narrowly defined than the common use of the word. Work is done on an object when an applied force moves it through a distance. In our English language, work is related to expenditure of muscular effort, but this is not same in the language of physics.

     A person that holds a heavy object does no physical work because the force is not moving the object through a distance. Work, according to the physics definition, is being accomplished while the heavy object is being lifted but not while the object is stationary. 

  

For Example:-

The absence of work is a mass on the end of a string rotating in a horizontal circle on a frictionless surface. The centripetal force is directed toward the center of the circle and, therefore, is not moving the object through a distance; that is, the force is not in the direction of motion of the object. However, work was done to set the mass in motion.

Mathematical Form:-

Mathematically, work is W = F.d Cos ø

Where F is the applied force and d is the distance moved, that is, displacement.

Cos thetha is angle in between F & d as shown in below figure.

Explanation:-

If work is done by a varying force, the above equation cannot be used. Figure shows the force‐versus‐displacement graph for an object that has three different successive forces acting on it. The force is increasing in segment I, is constant in segment II, and is decreasing in segment III. work performed on the object by each force is the area between the curve and the x axis. The total work done is the total area between the curve and the x axis.

For example, in this case, the work done by the three successive 

force is shown in below figure.

Work as Scalar Product:-

From equation which is present in  Reference heading (Mathematical form) Work is defined as scalar product of force and distance means (It has magnitude but no any specific direction)

W= F.X

Units of Work:-

There are different units of Work which are given below:-

1) The S.I unit is Joule (newton -meter).

2) In CGS system the unit is “erg”.

3) In British system the unit is “foot pound”.

 Special cases of Work:-

There are some cases which I am trying to explain them through figure (a), (b),(c).

Case # 1

When   ø=0 then Cos 0º= 1

W= Fd Cos ø

   = Fd Cos 0º=Fd (work is positive)

In figure (a) shows a man exerting a constant force F along the handle of a  lawn mower, which make an angle with the horizontal. The horizontal displacement of the lawn mower, over which the force acts, is d and the work done is positive, figure also illustrates as the horizontal component of the force.

Case # 2

In figure (b) Shows a person holding a briefcase. The person must exert an upward force, equal in magnitude to weight of the briefcase, but this force does no work, because the displacement over which it acts in zero In figure (c), where the person in (b) is walking horizontally with constant speed , the work done by person on the briefcase is still zero, but now because the angle between the force exerted and the displacement is 90 degree (F is perpendicular to d) and Cos 90º =0.

Conclusion OF Above Cases:-

In figure (a) work done occurs by constant force. A person pushes a lawn mower with constant force and we can clearly see in the figure the component of force is parallel to the displacement to each other.

If we discuss Case# 2 in simple words that no work is done because both F and displacement are perpendicular to each other, As we know when anything is perpendicular so angle will be 90 degree and finally  Cos 90º is equal to zero.