Question
3 A gardener pushes a lawnmower over his lawn. He exerts an average force of 24N. By the time he has finished mowing he has done 2160J of work. (a) (i) How far has the gardener pushed the mower in doing this work? You are advised to show your working out.
Answer
4.5
(227 Votes)
Quentin
Master · Tutor for 5 years
Answer
90 m
Explanation
The work done on a system is equal to the force (F) applied times the distance (d) over which the force is applied times the cosine of the angle (θ) between the force and the direction of displacement, mathematically represented as W = F * d * cos(θ). The cosine of the angle between the direction of the force and the direction of displacement for the lawnmower is cos (0) = 1, because the force and the displacement dimensions are in the same direction (horizontally across the lawn) . Hence θ = 0°. Therefore, the equation is simplified to W = F * d. The aim here is to solve for the distance travelled (d=?). The force exerted by the gardener (F) is 24 N and the workdone (W) equals 2160 J. Therefore, d = W/F = 2160 J / 24 N.