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BD 1 of 5 EGG 131L, Lab 8 Manual, 90 points Archimedes' Principle Name: 1. Objective 1.1 Study Archimedes' principle. 1.2 Determine the density of two solids and a liquid by using Archimedes' principle. 2. Apparatus Hanging scale, beaker, aluminum block, plastic cylinder, water, 99% alcohol, and thread. 3. Theory Density is defined as mass per unit volume that has a metric unit of kg per cubic meter. Grams per cubic centimeter i.e. g/cm actually is widely used as the unit of density. The densities for objects with regular shapes are easily to be determined. For objects with irregular shapes since their volume is very difficult to be determined, Archimedes' principle is a simple method to be used to determine their densities. Archimedes' principle states: a body immersed in a fluid is buoyed up by a force that equals the weight of the displaced fluid. Taking the buoyancy as FB, the volume of the displaced liquid as VL, and the weight density of displaced liquid as di, then from FB = VL dL, we have FB VL = dL (8.1 ) If the liquid is the regular water that has a density of 1 gram/cm', and FB is measured in unit of gram, the magnitude of volume is just simply equal to FB in unit of cm'. Thus by measuring the buoyant force FB, the volume of an object immersed in water can be determined, no matter how irregular the shape of the object is. Consider now an object that sinks in water. If its true weight (measured in grams for this lab) in air is WA, while its apparent weight (the weight in water) is Ww. Then the buoyancy is FB = WA - Ww. (8.2) This buoyancy numerically is the volume of the displaced water, and it is also the volume of the EGG 131L, Lab 8 Manual, 90 points submerged object. If the mass of a object is measured in grams which is equal to WA, then the density of the object is: mass WA d = volume WA - WW (8.3) TECHSPRAY PROPYL4. Preparation 4.1 Read the following article to get some idea about a simple pendulum https://www.livescience.com/58839-archimedes-principle.html 1 3 of 5 principle - Wikipedia 4.2 Watch the following videos to see a demonstration for this lab. https://www.youtube.com/watch?v=_p-hwElkrlk https://www.youtube.com/watch?v=05WkCPOR1j4 N EGG 131L, Lab 8 Manual, 90 points 5. Procedure 5.1 Determine density of aluminum block Hang the aluminum block from the balance by a thread to get the true weight of WA. Then sink it in water to get the apparent weight (the weight in water) Ww. Use formula (8.3) to get the density. The true value of density for aluminum is 2.7 g/em3. 5.2 Determine density of a plastic cylinder Since the density of plastic is smaller than that of water, it will not totally immerse underneath the water. A sink with a weight of WSA (also this is its mass numerically) is needed. The density formula will be modified as: d = W PA (8.4) (Wp + Ws)A -(Wp + Ws)w -(WSA - WSw) where WPA is the mass numerically of the plastic cylinder in air, (Wp + Ws)A is the total weight of the sinker and the plastic cylinder ( they are tied together) in air, (Wp + Ws)w is the total weight of the sinker and the plastic cylinder in water. WSA is the weight of sinker itself in air, while Wsw is the weight of sinker itself in water. The true value of the density for the plastic cylinder is: 0.95 g/cm'. 5.3 Determine density of alcohol The density of a liquid also can be determined by using Archimedes' principle from weighing an object (using the sinker). The formula is: d = . WSA- W SL (8.5 ) WSA- W SW where WEL the weight of sinker in the alcohol. The true value of density for the alcohol in this lab is: 0.81 g/cm'. w EGG 131L, Lab 8 Manual, 90 points Lab Report 1. Purpose (10 points)EGG 131L, Lab 8 Manual, 90 points Lab Report 1. Purpose (10 points) 2. Data 2.1 Aluminum Block (6 points) WA: Ww: 2.2 Plastic Cylinder (10 point) WPA: WSA: Wsw: (WP + WS)A: (Wp + Ws)w: 2.3 Alcohol (4 points) WSL: 3. Calculation for Densities (24 points)EGG 131L, Lab 8 Manual, 90 points 4. Conclusion (16 points) 5. Application (20 points) Use Archimedes' Principle to solve the following problem. You need show the procedure. An iceberg is floating on the sea. The density of ice is 0.917 g/cm', and the density of seawater is 1.03 g/cm'. If the portion of the iceberg above the sea is 1000 ft'. How many cubic feet are under the sea?BD 1 of 3 Lab & Raw Data 1 . Aluminum Block Weight in air - Scale Reading = WA = 62 grams 5 block reading Ww = 40 grams 5 beaker Weight in water water 2. Plastic Cylinder ( a ) reading WSA = 70 grams Sinker weight in air SinkerP. 2 18 - reading WPA = 23 grams Plastic- cylinder weight in air Plastic Cylinder ( C ) ILL reading sinker Wow = 62 grams Sinker's weight in water vate reading . ( Wp + Ws ) w = 59 grow plastic cylinder and sinker together in water water Plastic cylinder SinkerP.3 3. Alcohol Reading : Wsc = 63 grams Sinker Sinker Weight In alcohol Alco hox