A gardener pushes a lawn roller on a rough surface. He applies a force of 150 N over a distance of 5 m. After he gets tired and his applied force reduces linerly with distance to 75 N. The total distance moved is 10 m. Plot the force applied by the gardencer and the frictional force, which is 75 N versus displacement. Calculate the work done by t he two forces over 10 m.

Explanation

Plot of the force `vecF` applied by the gardener and the oposing frictional force f vs displacement

At `x=10 m, F=75N (ne0)` frictional force, `f-(|vec|=75N.` It opposes motion and acts in a direction opposite to `vecF` it is therefore shown on the negative side of the force axis. The work done by t he Gardener is
`W_(F)` = Area of rectangle ABCD+Area of trapezium CEID
`=150xx5+1/2xx(150+75)xx5`
`=750+462.5=1312.5J`
Woek done by frictional force is
`W_(f)=` Area of rectangle AGHI
`=(-75)xx10=-750J`
The area on the negative side of the force axis has a negative sign