Halliday, Resnick & Walker — Oscillations: Problem Problem_110

Competition diving board. A competition diving board sits on a fulcrum about one-third of the way out from the fixed end of the board (Fig. 15.45a). In a running dive, a diver takes three quick steps along the board, out past the fulcrum so as to rotate the board’s free end downward. As the board rebounds back through the horizontal, the diver leaps upward and toward the board’s free end (Fig. 15.45b). A skilled diver trains to land on the free end just as the board has completed 2.5 oscillation cycles during the leap. With such timing, the diver lands as the free end is moving downward with the greatest speed (Fig. 15.45c). The landing then drives the free end down substantially, and the rebound catapults the diver high into the air. Figure 15.45d shows a simple but realistic model of a competition board. The board section beyond the fulcrum is treated as a stiff rod of length \(L\) that can rotate about a hinge at the fulcrum, compressing a spring under the board’s free end. If the rod’s mass is \(m = 20.0 \text{ kg}\) and the diver’s leap has the flight time \(t_{fl} = 0.620 \text{ s}\), what spring constant \(k\) is required of the spring for a proper landing?