Explain with graphs the difference between work done by a constant force and by a variable force.

Explanation

Work done by a constant force : when a constant force F acts on a body , the small work done (dW ) by the force in producing a small displacement dr given by the relation .
` dW = (f cos theta ) dr `
The total work done in producing a displacement from initial position `r_i` to final position ` r_f ` is ,
` W= int_( r_i )^( r_f) dW`
`W= int_(r_i )^(r_f) ( F cos theta ) dr = ( f cos theta ) int_(r_i )^(r_f) dr = (F cos theta ) ( r_(f) - r_i)`
The graphical reprentation of hte work done by a constant force is shown in figure given below the area under the graph shows the work done by the constant force .

work done by a variable force : when the componant of a variable force F acts on a body the small work done (dW ) by the force in producing a small displacement dr is given by the relation

dW =` F cos theta dr ` [ F cos ` theta` is the component of the variable force F ]
where F and ` theta` are variables . the total done for a displacement from initial position `r_i` to final position `r_f ` is given by the relation ,
` W= int_( r_i )^(r_f) dW = int_(r_i)^(r_f) F cos theta dr `
A graphical representation of the work done by a variable force is shown in figure given below , the area under the graph is the work done by the variable force.