Work

Work

This page is continuing on from Energy page.  It is going to discuss the idea of work, what it relates to and how it fits into the principle of energy.  The word work is used in general terms to describe the process of doing a job for money and often said through a sigh and gritted teeth,  but in actual scientific terms this is not what work is. 

Therefore work is something that occurs all around but is never considered as such. The unit of work is measured in JOULES (J) and is defined as the amount of work done when a force of one newton acts through a distance of one meter in the direction of its application.  hence 1J = 1Nm

Before moving onto any maths lets consider what work is and how we can relate it.  It is important to be able to distinguish what work is. 

Scenario 1

A teacher applies a force to a wall and becomes exhausted.  

Is this work?  

No.  The wall has not been displaced by the force applied therefore no work has been completed.  It is possible to relate this back to newtons laws though.  The lack of movement means that for the force being applied and equal force is reacting back.

Scenario 2

A book falls off a table and free falls to the ground.

Is this work?

Yes.   There is a force (gravity) which acts on the book which causes it to be displaced in a downward direction.  the book has potential energy and as it falls the potential energy changes to kinetic energy. 

Scenario 3

A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed. 

Is this work?

No.  There is a force (the waiter pushes up on the tray) and there is a displacement (the tray is moved horizontally across the room). Yet the force does not cause the displacement. To cause a displacement, there must be a component of force in the direction of the displacement.

Scenario 4

A rocket accelerates through space.

Yes.  This is an example of work. There is a force (the expelled gases push on the rocket) which causes the rocket to be displaced through space.

Note:

(a)  No work is done unless there is both resistance and movement.

(b)  The resistance and the force needed to overcome it are equal.

(c)  The distance moved must be measured in exactly the opposite direction to that of the resistance being overcome.

The more common resistances to overcome are friction, gravity and inertia.

When considering the equation for work done there are a few variances but the main notion is :

Where:

mechanical work done (J) = Force required to overcome the resistance (N) x distance moved against the resistance (m)

The other notions for this equation are:

WD against friction = friction force x distance moved

WD against gravity = weight x gain in height

WD against inertia = inertia force x distance moved

The diagram below shows where and how the equation is formed.

Work Graph

The work done by a force  can be represented by a graph and is more useful when there are variable forces.  The area under the graph shown shaded represents the work done.  When determining the area under a variable graph use the ‘mid-ordinate rule’  The more ordinates made the more accurate the result.

A motor supplies a constant force of 1KN which is used to move a load a distance of 5m. The force is then changed to a constant 500N and the load is moved a further 15m.  Draw the force/distance graph for the operation and from the graph determine the work done by the motor.

WDT = area under force/distance graph

WDT = area ABFE  + area CDGF

WDT = (1000N x 5m)  +  (500N x 15m)

WDT = 5000J + 7500J

WDT = 12500J   or   12.5KJ

Springs are represented slightly differently.  But a graph can still be drawn.

A spring extended by 20 mm by a force of 500 N may be represented by the work diagram shown below:

WD = shaded area

WD = 1/2  x  base  x  height

WD = 1/2  x (20x10-3) m x  500 N  = 5 Joules

(NB: the small -3 is a power and therefore should be written to 

the top of the line but this program will not allow it)

To recap:

The unit of work is the JOULE

Work Done =  Force  x  Distance

1 Newton Meter  =  1 Joules

Work can be represented as a graph where the work done is the shaded area under the line.