When a ship floats in still water, what two main forces must perfectly balance each other?

When a ship floats in still water, the two main forces that must perfectly balance each other are the gravitational force acting downwards and the buoyant force acting upwards. This perfect balance ensures the ship remains stationary at a constant water level.

The gravitational force, commonly referred to as the ship's weight, is the force exerted by Earth's gravity pulling the entire mass of the ship downwards. Its magnitude depends directly on the total mass of the ship, including its hull, machinery, cargo, and crew. This force always acts vertically downwards through a specific point known as the ship's center of gravity.

The buoyant force is the upward force exerted by the water on the submerged portion of the ship. This force originates from the principle that water pressure increases with depth; thus, the upward pressure exerted on the bottom surfaces of the ship is greater than the downward pressure on its top submerged surfaces, resulting in a net upward push. According to Archimedes' Principle, the magnitude of this buoyant force is exactly equal to the weight of the volume of water that the ship displaces. This force always acts vertically upwards through the center of buoyancy, which is the center of gravity of the displaced water.

For a ship to float stably and motionless in still water, it must be in a state of vertical equilibrium. This means that the net vertical force acting on the ship is zero. Therefore, the upward buoyant force must be precisely equal in magnitude and opposite in direction to the downward gravitational force. If the buoyant force were less than the gravitational force, the ship would sink. If the buoyant force were greater, the ship would rise further out of the water until the displaced volume of water decreased enough to balance its weight, thereby re-establishing equilibrium.