Buoyancy and Archimedes’ Principle

 Name: Date: Purpose: To understand buoyancy and Archimedes’ principle. Think about it: do you feel heavier or lighter when you swim? Theory: An immersed body is buoyed up by a force equal to the weight of the fluid it displaces. As you can see, by looking at the scales in the above figure, we can conclude that the object weighs less in water. Density is defined as the ratio of mass to volume. In equation form, this can be written as: Density = Mass/Volume Water has a density of 1 kg/liter or 1 kg/L. The human body has a density very close to that of water. Therefore, a person with a mass of 80 kg, for example, will have a volume roughly equal to 80 liters. Let us see what happens if we put these values into our Density equation: Question: What is the (approximate) density of a person with a mass of 80 kg? Answer: Density = Mass/Volume Density = 80 kg/80 L = 1 kg/L Because the density of the human body closely matches that of water, it is relatively easy for us to float on water. Example: Let us look at an example that illustrates some of the physics of immersed objects. Question: Charlie weighs 150 pounds. He goes for a swim and dives into the deep end of the pool. What forces does he experience while submerged? Solution: We first covert Charlie’s weight from pounds (lb) to kilograms (kg): Charlie’s weight = 150 Ib (pounds) Conversion factor: 1 kg = 2.205 Ib Charlie’s mass = 150 Ib x 1 kg/2.205Ib = 150 kg/2.205 = 68 kg Next, we find the force of gravity on Charlie: Charlie’s weight (W), in the units of newtons, is the force of gravity pulling down on him. From Newton’s second law this force is given by: F = ma where m = 68 kg (which is Charlie’s mass) a = 10 m/s2, (the acceleration due to gravity) Therefore, W = mg = 68 kg x10 m/s2 = 680 N Charlie’s volume is approximately 68 liters. When Charlie is immersed in water, he displaces (or his body pushes aside) a volume of water equal to his volume. In other words, Charlie displaces 68 liters of water, when submerged. Applying our knowledge of the density of water, we see that the mass of this displaced water is also 68 kg. Therefore, the weight of the displaced water is 680 N. While gravity pulls down on Charlie with a force of 680 N, the water pushes up on him with an equal and opposite force of 680 N. This upward force exerted by fluids on immersed objects is called the buoyant force. These two forces cancel out, and Charlie essentially feels weightless in water.