Final answer:
The maximum buoyant force allows a ship to carry a load nine times its own weight, and safety limits like those on bridges are based on similar principles of maximum allowable weight that will not compromise structural integrity.
Step-by-step explanation:
A sticker or placard on the boats displays safety information, such as maximum weight or number of people the boat can carry safely. Whether 20 men with a sum weight greater than 3,500 pounds exceed the safety limits for water taxis depends on the buoyant force the boat can exert, which is determined by the displacement of water.
The maximum buoyant force is a crucial concept here. It is ten times the weight of the steel used to construct the ship, meaning that the ship can carry a load nine times its own weight without the risk of sinking. This capacity is calculated based on the Archimedes' principle, where the buoyant force is equal to the weight of the water displaced by the ship's hull. Therefore, when considering the safety limits, you should compare the total weight of the men to the ship's capacity to carry a load nine times its own weight.
In the context of safety limits, similar principles apply to other structures and situations. For instance, load limit signs on bridges warn of the maximum weight they can safely support, and there are occupancy limits for rooms as well as limits to what can go into an electron orbital in chemistry.