Sir Lancelot rides slowly out of the castle at Camelot and onto the 12.0-m-long drawbridge that passes over the moat (?Fig. P11.44?). Unbeknownst to him, his enemies have partially severed the vertical cable holding up the front end of the bridge so that it will break under a tension of 5.80 X 103 N. The bridge has mass 200 kg and its center of gravity is at its center. Lancelot, his lance, his armor, and his horse together have a combined mass of 600 kg. Will the cable break before Lancelot reaches the end of the drawbridge? If so, how far from the castle end of the bridge will the center of gravity of the horse plus rider be when the cable breaks?
Solution 46P Step 1: Length of the bridge = 12.0 m Mass of the bridge m = 200 kg (W = m g) B B B Center of gravity of the bridge is at 6. 0 m Combined mass of Sir Lancelot, his armor, and his horse m = 600 kg L (W Lm gL 3 Maximum tension can be applied T = 5.8 x 10 N 2 Acceleration due to gravity g = 9.8 m/s Step 2: Weights of the bridge and Sir Lancelot act downward and the tension on cable acts upward. Therefore the torque produced by the tension = torque by the rider + torque about the hinge of the bridge C = +L B ---(1) Step 3: If Sir Lancelot at the end of the bridge, = W x 12 L L B = W B6 C = Tx12 T x12 = W x L + W x 6 B---(2)