91Ó°ÊÓ

The given data is listed below as-

• The displacement is, $s=2.75m$
• The mass of the painter is, $m=75kg$
• The angle that the ladder makes with the wall= $30°$

Work done on a particle by a constant forceduring a linear displacement is given by

Now, the force due to gravity on the painter is downwards.

The displacement is along the ladder as shown in fig. below:

From the above Fig., it can be seen that

$\cos 30°=\frac{AC}{AB}$

Here, AC=h and AB=s, then it can be written as below:

$h=s.\cos 30°$

For$s=2.75m$

$$\begin{gathered} h=2.75m×0.866 \\ =2.38m \end{gathered}$$

Now, work done by gravity on the painter is given by

$W=-mgh$

Here, m isthe mass of the painter, g is the gravitational constant and h is the height of the wall.

For $m=75kg$, h=2.38 m and$g=9.8m.s^{-2}$

$W=-mgh$

$$\begin{gathered} W=-\left(75kg\right)×\left(9.8m.s^{-2}\right)×\left(2.38m\right) \\ =-1750J \end{gathered}$$

Thus, the total work done by gravity on the painter is -1750 J.

Thus, the work done by the gravity on the painter does not depend upon whether the painter climbs at constant speed or accelerates up the ladder.