An underwater buoy is anchored at the seabed with a cable,...

An underwater buoy is anchored at the seabed with a cable, and it contains a total mass of $250 \mathrm{~kg}$. What should the volume be so that the cable holds it down with a force of $1000 \mathrm{~N} ?$

Key Concepts

Archimedes’ Principle

This principle states that any object submerged in a fluid is buoyed up by a force equal to the weight of the fluid that the object displaces. It forms the foundation for understanding buoyancy in fluids, and it is essential for calculating how much upward force a submerged object experiences.

Buoyant Force

The buoyant force is the upward force exerted by a fluid on an immersed object, and it can be calculated by multiplying the density of the fluid, gravitational acceleration, and the displaced volume. This concept is crucial in problems where the net force due to buoyancy must be balanced with other forces, such as weight or applied forces like cable tension.

Force Equilibrium

In statics, force equilibrium refers to the condition where all forces acting on a body are balanced, so that the net force is zero. In buoyancy problems, this involves setting the difference between the buoyant force and the gravitational force equal to any additional forces (for example, tension) to achieve a state of equilibrium.

Density of Fluid

The density of a fluid is the mass per unit volume of the fluid and is a key factor in buoyancy calculations. In an immersion scenario, knowing the fluid’s density allows you to determine the weight of the displaced fluid and consequently the magnitude of the buoyant force acting on the object.

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