Question

Sir Lancelot rides slowly out of the castle at Camelot andonto the 12.0 m long drawbridge that passes over the moat (Fig11.28). Unbeknownst to him, his enemies have partially severed thevertical cable holding up the front end of the bridge so that itwill break under a tension of 5.80 x 103 N. The bridgehas mass 200 kg and its center of gravity is at its center.Lancelot, his lance, his armor, and his horse together have acombined mass of 600 kg. Will the cable break before Lancelotreaches the end of the drawbridge? If so, how far from the castleend of the bridge will the center of gravity of the horse plusrider be when the cable breaks?

Sir Lancelot rides slowly out of the castle at Cam

Answer 1

The question requires the application of physics principles to determine if a cable supporting a drawbridge will break under the weight of Sir Lancelot and his horse. By combining the masses and calculating the forces, we can use the principles of moments to find the point of failure.

Step-by-step explanation:

The scenario presents a physics problem involving statics and the breaking tension of a cable. Given the mass of the drawbridge, Sir Lancelot, and his equipment, we must determine whether the cable will break and, if so, the position of the center of gravity of Sir Lancelot and his horse relative to the castle end of the bridge when the breakage occurs.

Firstly, we calculate the total weight exerted on the bridge by adding the weight of the drawbridge (200 kg) to the weight of Lancelot and his equipment (600 kg). The total force acting downward is then the combined weight multiplied by the acceleration due to gravity (g ≈ 9.81 m/s2). To determine whether the cable breaks, we must consider where the combined center of gravity of Lancelot and his equipment will be when the tension in the cable reaches its failure point of 5.80 x 103 N.

Using the principles of moments or torque, we can set up an equation balancing the anticlockwise moments (due to the weight of Lancelot and his equipment) and the clockwise moments (due to the weight of the drawbridge, when balanced by the tension on the cable). Since Lancelot moves at a slow pace, dynamic effects can be ignored, simplifying our calculation. If the weight of Lancelot and his horse creates a moment that exceeds the maximal tension the cable can handle, it will snap at that point.