Work-Introduction
A. Work
The term work as understood in everyday life , has a different meaning in scientific sense. The term work is considered to be a synonym of labor , effort, etc. For example, when a student sits at his/her chair studying a book, he/she is not doing any work in the scientific sense. In scientific sense, work is said to be done when a force acting on a body displaces it.
Thus, The product of force and displacement of the body in the direction of the force is known as Work.
Mathematically,
Work(W)=Force(F) x Displacement(d) ( in the direction of the force )
W=F.d
If ‘F’ is the applied force on a body and ‘d’ is its displacement in the direction of the force, the work done ‘W’ by the force will be given by
W=F. d ………….(i)
The SI unit of force is newton (N) and that of displacement is metre (m). From this equation(i), the unit of work is newton-metre (Nm), which is called joule (J).
Therefore, 1J =1N. 1m
=(1 kg x 1 m/s^{2}). 1 m (Therefore 1 N=1 kg x 1 m/s^{2})
=1 kgm^{2}s^{2}
Thus ,one joule of work is said to be done when one Newton force displacement a body through one metre in its own direction.
Kilo joule (KJ) and mega joule (MJ) are the bigger units of work . The relation between them is as follows-
1KJ = 10^{3} joules
1 MJ = 10^{6} joules or 10^{3} KJ.
In C.G.S. system work is measured in erg. 1 erg work is that in which 1 dyne force covers a distance of 1 cm 1 dyne force is that which can produce an acceleration of 1 cms^{-2} in 1g mass.
1 Erg = 1 dyne cm
1 J = 10^{7} erg
We know that
1 J =1 Nm =1 kg m/s^{2}.m =1000g x 100 cm/s^{2}.100 cm =10^{7} g cm^{2} s^{-2} = 10^{7} dyne cm [Therefore 1 dyne = 1 gcms^{-2}] = 10^{7} erg [Therefore 1 erg =1 dyne cm] Thus, 1 j = 10^{7} erg |
Equation (i) indicates that W=0 when either F or d=0, That is force acting on a body must produce a displacement for the work is to done by the force. Thus for work to be done, the following Two conditions must be fulfilled;
1. A force must be applied, and
2.The applied force must produce a displacement in any direction expect perpendicular to the direction of the force.
In general , Work is done against friction and Gravity.
A. Work against friction
Force is to be applied to move, roll or drag a body over a surface of another body. While in motion , frictional force comes into action, which opposes or tends to oppose the motion of the body. The body sets in motion only if the applied force overcomes the frictional force.
Activity;4.1; To demonstrate work against friction
1.Let spring balance be attached to a wooden box. The box is kept on a table.
2. Now the box is pulled as shown in the figure.
A sliding body
It moves by a displacement ‘d’. Here, we have to apply force against the frictional force between the surface of the box and the table to set the box in motion. Thus, work is done against the friction.
B. Work against gravity
To lift a body to a height ‘h’, we have to apply force against the force of gravity. This is because the force of gravity always acts vertically downwards.
Lifting or throwing things upwards are examples of this work. Activity;4.2; To demonstrate work against gravity
A box of mass ‘m’ is raised to a height ‘h’ using a spring balance as shown in the figure.
The pointer of spring balance gives the force applied ‘F’ against the gravity. The product of the Force (F) and height (h) raised gives the work against gravity in this case.
Measurement of work
On the basis of the direction of motion of a body and the direction of force applied, the way of calculation of work done is determined. Study the following situations for the better concept. 1. When a body moves in the direction of force applied;
In the above conditions (work against friction and work against gravity ) the direction of motion of body and the direction of force applied are the same. In the both cases, we can use :-
Work done (W)= Force(F) x Displacement (d)