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Understanding the concept of gravitational force is crucial when analyzing the buoyancy principle. Essentially, gravitational force is the pull that Earth exerts on any object with mass. This force is responsible for keeping us anchored to the ground and is also a determining factor in how objects float or sink in water.

In the context of our exercise, the athlete's weight of 900 N (newtons) is a direct measure of the gravitational force, since weight is the force of gravity on an object. Surprisingly, even an additional upward force of 20 N is needed to keep the athlete buoyant. This points to a critical relationship between gravitational force and buoyancy, namely that an object will sink if the gravitational force on it exceeds the buoyant force of the fluid it is in.

In practical terms, when you step onto a scale, the reading you see is the gravitational force acting on your body. For objects submerged in a fluid, we use the concept of gravitational force to understand how much force is needed to counteract this pull in order to achieve flotation. For our athlete, his gravitational force defines the starting point for calculating not just buoyancy, but also his volume and density in the pool.

The principle of volume displacement is a fundamental aspect of buoyancy, which Archimedes notably described centuries ago. The principle states that any object, partially or fully submerged in a fluid, displaces a volume of that fluid equal to its own volume.

Hence, when our athlete is submerged in the pool, he is displacing an amount of water that is equivalent to his body's volume. This displaced volume of water has a weight, and according to Archimedes' principle, this weight is equal to the buoyant force acting upward on the athlete.

To calculate volume displacement in this case, we use the total force required to keep the athlete buoyant in fresh water (the gravitational force plus the additional upwards force) and divide it by the product of gravity's acceleration and the density of water. This tells us the volume of water which, if removed, would be equivalent to the volume of the athlete himself. Understanding volume displacement allows us not only to grasp why objects float or sink, but also to calculate their volumes under different conditions, an essential step in determining factors such as average density.

Average density is the ratio of an object's mass to its volume. Calculating an object's average density helps us predict whether it will float or sink in a fluid. The average density is a fundamental concept in the study of fluid mechanics and buoyancy.

In our buoyancy problem, to calculate the athlete's average density, we first need to establish his mass from the given weight (force due to gravity). We then calculate his volume from the previous steps. By dividing the mass by the volume, we find the athlete's average density. If this density is greater than that of the fluid he is in, he will sink; if it is less, he will float.

Interestingly, the average density tells us about the distribution of mass throughout an object's volume. For humans, this varies individually, which is why some people float more easily than others. In the case of our athlete, his average density turns out to be more than the density of the water, evidenced by the need for an extra force to keep him afloat. This simple calculation of average density reveals important insights into the principles of buoyancy.