A woman pushes a trunk on a railway platform which has a rough surface . She applies a force of 100 N over a distance of 10 m . Thereafter ,she gets progressively tired and her applied force reduces linearly with distance to 50 N . The total distance through which the trunk has been moved is 20 m . Plot the force applied by the woman and the frictional force , which is 50 N versus dispalcement Calculate the work done by the two forces over 20 m .

Explanation

Frictional force `|vec(f)| = 50 N ` exerted opposed in force and opposes the motion .So it is the negative side of force .It is shown in figure .

Work done by the woman is ,
`W_(F) = { "Area of ractangular AbCD" }+ {"Area of trapezium CEID"}`
` = AD xxAB +1/2 (CD +EI) xxDI`
` = 10 xx 100 +1/2 (100+50)xx(20-10)`
`=1000 +1/2 xx150 xx10`
` = 1000 + 750`
= 1750 J
Work done by friction force ,
`W_(f) = "Area of rectangular AGHI"`
` = AG xx GH`
` = - 50 xx 20`
` = - 1000 J `
The area on the negative side of the force axis has a negative sign .