Work done by a variable force

Work Done by a Variable Force

Variable force:

“ If the magnitude or direction of a force changes, then the force is said to be a variable force”.

Example:

The force exerted by a spring increases with the amount of stretch.

Explanation:

Fig shows the path of the particle in the x-y plane as it moves from point ‘a’ to ‘b’. The path has been divides into a short intervals of displacements ∆d1, ∆d2,…….,∆dn. F1,F2,……..Fn are the forces acting during these intervals.

During each small interval, the force is supposed to be approximately constant. So the work done for the first interval can then be written as.

∆W1 = F1 . ∆d1 = F1 CosӨ1 ∆d1

And in the secod interval,

∆W2 = F2 . ∆d2 = F2 d2 Cos Ө2 ∆

Ans so on for the ntʰ interval,

∆Wn = Fn . ∆dn = Fn CosӨn ∆dn

The total work done in moving the object can be calculated by adding all these terms.

Graphical Method:

The work done can also be calculated by plotting a graph between F CosӨ and d. The graph is of irregular shape. The value of Cos Ө at the start of each a large number of vertical strips.

Each strip is a thin rectangle. The length of any these rectangles is of CosӨ and with is equal to ∆d. So area of strip is ,

Area of rectangle =( F CosӨ) (∆d)

We divide the total displacement from point ‘a’ to point ‘b’ into very large Number of equal intervals so that ∆d→ 0 or n →∞ .

Then

Thus the total work done by the variable force in moving a partical from point ‘a’ to point ‘b’ is equal to the area under the curve between ‘F’ Cos Ө and ‘d’ as shown in above fig.

View more on psalmfresh.blogspot.com for more educating and tricks article Thank you