Answer
13.1 J
Work Step by Step
The work the gravitational force does on the ball will be W = –$\Delta U$ = –$mg\Delta h$.
The problem gives us the mass $m$ = 5.00 kg and we know that $g$ = 9.8 m/s², but we need to find the change in height $\Delta h$. By using the length of the rod L = 2.00 m and the angle $\theta _{0}$ = 30.0$^{\circ}$, we find that $\Delta h \approx$ –0.268 m (See attached picture for process).
Now we just plug in our values:
W = –$\Delta U$
= –$mg\Delta h$
= – (5.00 kg)(9.8 m/s²)(–0.268 m)
= 13.1 J
