91Ó°ÊÓ

To determine the distance over which the force exerts, divide the value of the lawn area with the width of the mower.

Also, the angle between the force and displacement is zero because the force is parallel to the displacement.

Given data:

The pushing force is\(F = 15\;{\rm{N}}\).

The area of the lawn is\(A = 10\;{\rm{m}} \times 20\;{\rm{m}}\).

The width of the mower is\(w = 50\;{\rm{cm}}\).

The relation of work done is as follows:

\(\begin{aligned}W &= Fd\\W &= F\left( {\frac{A}{w}} \right)\end{aligned}\)

On plugging the values in the above relation,

\(\begin{aligned}W &= \left( {15\;{\rm{N}}} \right)\left( {\frac{{10\;{\rm{m}} \times {\rm{20}}\;{\rm{m}}}}{{50\;{\rm{cm}} \times \frac{{1\;{\rm{m}}}}{{100\;{\rm{cm}}}}}}} \right)\\W &= 6000\;{\rm{J}}\end{aligned}\)

Thus, \(W = 6000\;{\rm{J}}\) is the work done on the lawn.