Archimedes' Principle Of Flotation

ARCHIMEDE'S PRINCIPLE OF FLOTATION Archimedes (c. 287 BC to 212/211 BC) lived in the Greek city-state of Syracuse, Sicily, up to the time that it was conquered by the Romans, a conquest that led to his death. Of his works that survive, the second of his two books of On Floating Bodies is considered his most mature work, commonly described as a tour de force. More than 2000 years ago, Archimedes noticed that objects seem to weigh less when they were placed in water. This effect produced by liquid or gas causes objects to float. When an object is placed in water, the water exerts an upward force or the upthrust upon the object. This upthrust is the force produced by water in reaction to the force of the weight of the object that is introduced in water. This upthrust or the upward force is termed as Buoyancy. Water puts pressure from all sides of the object to support its weight. However, the water pressure is highest at its deepest end. ARCHIMEDES' PRINCIPLE:

WHEN AN OBJECT IS IMMERSED IN A FLUID, THE UPTHRUST ON THE OBJECT IS EQUAL TO THE WEIGHT OF THE FLUID DISPOLACED.

The buoyancy acting on the object due to water must exactly counteract the weight of the object, i.e. the two have equal magnitude. So, a partially immersed object floats in a liquid when the buoyancy acting on it equals the weight of the object. A large ship at sea floats precisely because the weight of the seawater it displaces, i.e. buoyancy acting on the ship, equals the total weight of the ship. For a solid piece of iron, even if Buoyancy is maximized by fully immersing it in water, its weight always exceeds the Buoyancy of water. That is why it sinks in water. An equivalent and useful criterion for flotation of any object is that it will float in a liquid, if the density of the object is less than that of the liquid. This is true, for example, for wood or ice, both of which have a lower density than water. A solid piece of iron sinks in water because the density of iron is greater than that of water. However, a thin walled, hollow ball of iron, with adequate volume of air trapped within it, floats in water. In this case, the trapped air has lowered the average density of the ball, so that it is less than that of water. A given object may sink in one liquid, but float in another liquid. For example, a solid piece of iron sinks in water, but it will float, partially submerged, in a pool of mercury. We can thus conclude that mercury must have a higher density than iron, which is true. THE LAW OF FLOTATION: A floating object displaces its own weight of the fluid in which it floats. BOUYANCY OF AIR AND GASES: Air or any gas surrounding an object also behaves like a liquid, and exerts buoyancy upon an object. As a result, the apparent weight of an object in air is slightly less than its “true weight” measured in a vacuum. For many objects we deal with, this buoyancy effect due to air - which equals the weight of the air displaced by the

object, is quite small when compared to the overall weight of the object itself. So, we normally tend to ignore the effects of buoyancy due to air. However, the buoyancy of air becomes strikingly evident when one lets go of sealed, helium filled balloon. It doesn’t just float in air, but rapidly ascends, defying earth’s gravity! Clearly, in this case, the buoyancy due to air must exceed the total weight of the balloon, thereby causing a net upward force on the balloon, and enabling it to accelerate upwards! This is a vivid demonstration of the upward direction of buoyancy. A strange observation is that ,although an object made of Steel which is an alloy of iron, sinks in water, a steel or iron needle remains floating on the water surface. Can any of you students come up with an explanation for this strange fact?

Why boats float and elephants sink :buoyancy How does a boat or ship carrying hundreds of pounds worth of stuff float while that same stuff would sink to the bottom of the ocean if dumped overboard? How come when you're in a pool and you stretch your body out flat you float. But, if you wrap your arms around your legs and curl up into a ball you sink? Well, it all has to do with how much water is pushing against you and a little scientific principle called buoyancy or floatation. When you stretch out flat more water pushes against you since your body is laid out flatter The object must make room for its own volume by pushing aside, or displacing, an equivalent (or equal) volume of liquid. The object must make room for its own volume by pushing aside, or displacing, an equivalent (or equal) volume of liquid. The object is exerting a downward force on the water and the water is therefore exerting a upward force on the object. Of course the floating object's weight comes into play also. The solid body floats when it has displaced just enough water to equal its own original weight. This principle is called buoyancy. Buoyancy is the loss in weight an object seems to undergo when placed in a liquid, as compared to its weight in air. Archimedes' principle states that an object fully or partly immersed in a liquid is buoyed upward by a force equal to the weight of the liquid displaced by that object. From this principle, he concluded that a floating object displaces an amount of liquid equal to its own weight. *ships floating on water : Any change in the density of the surrounding water affects the level at which ships float. Fresh water is less dense than salt water. So a ship floats lower in fresh water than it does in salt water. Warm water is les dense than cold water , so a ship floats lower in the water if the temperature rises.

A boat loaded to its maximum in cold, salty water could float dangerously low if sailing in low warm water. To prevent this , all ships now have 'maxu\imum load' or Plimsoll lines marked on their side Referrence: http://www.spartechsoftware.com/reeko/Experiments/floating.htm

RELATIVE DENSITY OF A SOLID: Relative density of an object = mass of object mass of same volume of water The concept of relative density comes by comparing the density of an object to the density of water. It is calculated by weighing the object in air and then placing it in water. The amount of water that has been displaced when the object was placed in it is then weighed. This comparison when calculated, gives the relative density of the object. RELATIVE DENSITY OF A LIQUID: The relative density of a liquid measures: Mass of liquid mass of equal volume of water Also, Apparent loss in weight of object in liquid Apparent loss in weight of object in water An object immersed in meths [methanol] will experience less upthrust on it than if it was immersed in water. It is due to the fact that meths is less dense than water so the meths displaced by the object weighs less than the same volumes of water yet the volume displaced by it is greater than the volume displaced by water. This is again, due to the reason that meths is less dense than water therefore less heavier, so more volume of it will make for eg, a 2N weight than the volume of 2N of water. Hence, to displace this larger volume of meths the object floats lower in meths than in water. By comparing the density of an object with that of the fluid it is to be immersed in , it can be found whether it will float or sink in that fluid. The object will only float if its density is same or less than that of the fluid.

For eg: • Wood, petrol and ice will float in water • Hot water will float up in cold water • Hydrogen gas will float upwards in air • Hot air will float upwards in cold air • Steel will float in liquid mercury but sink in water CALCULATIONS ON ARCHIMEDES' PRINCIPLE AND FLOTATION: • •

Archimedes' principle applies to all objects immersed in liquid regardless of whether they are floating or not The Law of flotation, however, only applies to floating objects.

Both the Law and the Principle are concerned with weight of objects and fluids. However, when solving problems, one is often dealing with volumes. The connection between the weigh of a substance and its volume is : Mass = volume x density Weight = mass x g Therefore, __________________________ |Weight = volume x density x g| These equations should be sufficient in determining the floating ability of objects . Parts left out in this lecture upon Hydrometers and hot air balloons will be discussed in class. END OF LECTURE