Work is the force acting per unit displacement. It is a measure of displacement. Work is a scalar quantity as it is a dot product of two vector quantities. Some examples of work done are – riding a bicycle on a hill, carrying a trolley from one place to another, running from one end of a road to another, etc. Remember running across a field may result in zero work done as the displacement is zero in this case. The person running will return to his original position resulting in zero displacements.
Similarly, the work done by a weightlifter is zero as there is no change in displacement taking place. Therefore, work is mechanical energy used to lift, move, or do other activities with the object. The formula for the work done is given by
W = F. d cos θ
Where F = force applied on the body
d = displacement
θ = angle formed between force and displacement
There are two types of work – positive work and negative work.
Positive work
The equation W = F describes the work. d CosӨ.
When Ө is acute, i.e., Ө< 90°, work is positive.
Negative work
It happens when Ө is obtuse, i.e., Ө> 90°.
The angle between the force F and displacement S is 180°. Therefore, the work done by gravity on moving a body upwards is negative.
Every day we work differently on different tasks or activities. However, the amount of energy spent, labor done, and toil, are all synonyms of work. The work done is calculated in Joules. It is the amount of a unit force applied per unit displacement. In other words, 1N of force applied to cause a displacement of 1m. Therefore, the unit of work is Newtonmeter (Nm).
Work in measured in gases as
W = P ΔV
Here, W is the work done in expanding the volume of the gas in a piston.
Units of work
In SI, the base unit is Kg m² s⁻²
Kg m² s⁻² is the MKS unit.
The MKS stands for meterkilogramsecond.
The CGS (centimetergramsecond) unit for work is dynecm or erg.
Units of work are represented as









Some other units of work include horsepower, erg, footpound, kilowatthour, literatmosphere, footpoundal, etc. Work has the same physical dimension as that of heat. Therefore, units like BTU, calorie, therm, etc. are also units of work done. Conversions of units are given below














Solution
Force, F = 25 N
Displacement, dr = 15 m
Angle between F and dr, θ = 30o
Work done, W = Fdr cosθ
W = 25 x 15 x cos 30 = 25 x 15 x √3 /2 = 324.76 J
A moving body of 30kg has 60 J of KE. Calculate the speed.
Solution: KE = 0.5 mv2
60 = 0.5 x 30 x v2
60 = 15 v2
V = 2m/s
Calculate the energy possessed by a stone of mass 10kg kept at a height of 5m If 196 x102 J of energy were used to raise a 40kg boy above the ground, how high would he be raised?
Solution: The energy possessed by a stone of mass 10kg kept at a height of 5m = PE
PE = mgh = 10 x 5 x 9.8 = 490 j
196 x102 J = 40 x 9.8 x h => h = 50m