A man hauls a 20kg stone that is currently resting atop a 300 meter cliff up the mountain side to a height of 500 meters. He then casts the stone directly downwards until it reaches the very base of the mountain (0 meters). What is the total work done on the stone
+6251 The easiest way to do this is to use gravitational potential.
First the man does work on the rock hauling it from 300m to 500m.
This work is given by
\(W_1=m g \Delta h = 20 \times 9.8 \times (500-300) = 39200 J\)
Then Earth's gravity does work on the stone during the fall from 500m to 0m. Again this work is the difference in gravitational potential
\(W_2 = 20 \times 9.8 \times 500 = 98000J\)
\(\mbox{The total work is } \\ W_T=W_1+W_2 = 39200+98000 =137200J\)
