Lab #9 - Buoyant Force/Density Some Background: Why do some things float while others sink? The answer was discovered more than two thousand years ago by Archimedes, a Greek scientist who lived in Syracuse a Greek city on the island of Sicily. The king there wanted a new gold crown so he gave some gold to a gold smith and instructed him to make gold crown. The gold smith soon presented the king with a beautiful new crown. The king was very pleased. But then word came that the gold smith had kept some of the gold for himself, substituting a cheaper metal for the gold to keep the weight of the crown the same. How could the king find out if this were true? He could just break the crown apart to see, but if the crown was pure gold he would've destroyed it for nothing. The king sent for Archimedes who served as the kin's science advisor and asked him if there some non-destructive way to determine whethergrngt the crown really was made of pure gold. Now the density was known and Archimedes realized that they could determine whether or not the crown was pure gold by finding its density. To find its density Archimedes had to nd crown's weight and volume. The weight was already known, but finding the crown's volume and this was a problem. How do you find the volume of something with an irregular shape? At this time neither Archimedes nor anyone else knew how. Archimedes began thinking hard on how this might be accomplished, but he was unable to think ofanything. One day tired and frustrated, Archimedes decided to go down to the bathhouse and have a nice hot bath (In those days people didn't have bathtubs in their houses). The bathtub he chose was full to brim and so, as he lowered himself into the water, the tub overflowed. in that moment e had a realization: The water that was displaced (pushed out the tub) must have the same volume as the part of his body immersed in the water which meant he could measure the volume of the crown by lowering it to a container full of water and measuring the volume of the water that over owed. He was so excited by this realization that he ran back home shouting \"Eureka! Eureka!\" (He also forgot to put his clothes on). His realization that an object immersed in water would displace a volume of water equal to the object's volume got Archimedes to thinking about the question: why do some things oat and others sink? People already knew that the answer had to do with density {o'gu'y knew that if an object were less density than water it would float and that if it were denser than water it would sink, but no one knew why this was the case. That was the mystery. Archimedes wondered if his realization about how the volume of displaced water equaling the volume of a submerged object might provide an explanation. Driven by his curiosity, Archimedes used his imagination (plus logical thinking) to create the explanation we accept today. Using modern terms & concepts, Archimedes thinking went something like this: -_... ...,__... __...., .. _c.._e,___,..._. ..___, _......... ..e..._,...,...... ...._ _..._. M While objects denser than water sink and objects lighter than water float to the surface, water itself doesn't do either one. This is strange because water has \"Parcel\" 0f water weight, yet water itself doesn't sink. At right is a diagram showing a "parcel\" of water. It's just a volume I've \"dotted out\" to help make it easier to see. Archimedes' realization that water does not sink in water led to the further realization that something must be holding the water up. But what is this something? It turns out the upward force is provided by the pressure of the surrounding water. Using to today's terminology, we call it the Buoyant Force (Fa). Archimedes realized that because water neither sinks nor rises, the buoyant force acting on the "parcel" must equal the weight of the water in the parcel. Thus: FB = men. Archimedes' other realization that an object placed in water would displace a volume of water equal to its submerged volume led Archimedes to the further realization that the buoyant force on the object must equal the weight of the displaced water. This statement has become known as: Archimedes Principle of Buoyancy which can be summarized as: Fa = men msmcm. It explains how the fact that some things float and others sink depends on density. If an object is denser than water, then it will weigh more than the volume of water is displaces when placed into water. But the weight of the displaced water equals the buoyant force (Archimedes Principle) that pushes upward on the object. 50 the weight of the object is greater than the buoyant force in this case and so the object will sink. If an object isles denser than water, then it will weigh less than the volume of water it displaces. So the buoyant force is greater than the weight of the object and so the object will float. WWATER = F3 Objective: i) Determine the density of a variety of objects using Archimedes Principle Theory: The upward force exerted by a liquid on a submerged object is called the buoyant force. This force is the reason for the apparent weight loss experienced by submerged objects. Consider the object shown below. Scale Reading The weight experiences two forces: An upward force due to the spring in the scale and a downward force due to E weight. When you measure its weight using a spring scale, the tension of the spring must equal downward weight. The scale reading shows the tension of the spring. Therefore, scale reading = weight of the object. Let's call this weight "weight in air\". When the object is in water it experiences three forces; the downward weight, the upward tension in the spring scale and the upward buoyant force. We can measure the upward tension by reading the scale on the spring scale. Because ofthe buoyant force it will read less than it did when the weight was hanging in air. Thus the weight will appear to weigh less. Scale Reading The net force acting on the object is = (tension + buoyant force weight) When in equilibrium, net force = 0 (Tension + buoyant force weight) = 0 Therefore, tension = weight buoyant force The scale reading shows the tension ofthe spring and in this case, it is equal to (weight buoyant force). This value is less than the true weight and is called \"apparent weight\" or the weight of the object in liquid. Now we can calculate the buoyant force. The buoyant force is the difference between the weight in air and the apparent weight (weight in liquid). Buoyant force = (weight in air weight in liquid) '''' Equation lll The buoyant force is also related to the amount of liquid displaced bythe object. According to Greek scientist Archimedes, the buoyant force is equal to the weight of displaced liquid. Buoyant force = weight of displaced liquid Buoyant force = (mass of displaced liquid) x g Because mass = density x volume Buoyant force = (density of liquid) x (displaced volume) X g # (2) In this lab we are going to measure the buoyant force on an object using the above two equations and compare the values. What makes an object sink or float? Consider an object in water (or any liquid). There are 2 forces acting on the object; 1) Its weight (down) 2) Buoyant force (up) Whether an object will sink or oat in a liquid depends on how the buoyant force compares with object's weight. This, in turn, depends on the object's density. 1) Object will float when weight of submerged object is less than the buoyant force it would have when submerged. 2) Object will float when it is less dense than water (or liquid) When oating, buoyant force = weight of oating object. Physical Experiment: Now perform the actual experiment using density = mass/Volume 1) Choose one item from the table below and measure its mass in grams. 2) Then measure its mass in grams when totally submerged in water. 3) The density of the object is the mass from step 1 divided by the difference in masses from steps 1 & 2. a. Density = Mass in air/ (Mass in air Mass when totally submerged in water) 0 The kit comes with two spring scales, 0 to 500 g and 0 to 100 g. Use the most appropriate one for each object. Data Table 100 g weight (from kit) Mass in Air Grams Mass in Water Grams 82g Density Gm/cmAS 5 washers (from kit) 24g 10 or more paper clips (from home) 50 g weight (from kit) The large binder clip (from kit) A sheet of aluminum foil folded small with no air in the folds (from home) From the table below, identify the substance making up of each item. Solids Density Density in grams/cm^3 (g/cm^3 (g/cm3) Lead 11.37 Silver 10.57 Copper 8.92 Brass 8.90 Nickel 8.57 Iron 7.90 Aluminum 2.67 Marble 2.60 - 2.84 Granite 2.65 Rubber 1.10 - 1.19 Oak 0.80 Pine 0.35- 0.50 Steel 7.75-8.05