Download Archimedes' Principle and more Study notes Acting in PDF only on Docsity! 1 Archimedes’ Principle Equipment Qty Item Parts Number 1 Force Sensor PS‐2104 1 Lab Jack SE‐9373 1 Beaker SE‐7288 1 250 mL Graduated Cylinder 1 Large Rod ME‐8738 1 Small Rod ME‐8988 1 Double Rod Clamp ME‐9873 1 Wooden Cylinder 2 Metal Cylinders Purpose The Purpose of this activity is to show some basic properties of the buoyant force. Namely that the buoyant force is a function of the density of the fluid, that the buoyant force is equal to the weight of the fluid displace by a submerged or floating object, and that the apparent weight of a submerged object is the difference between its weight and the buoyant force acting on it. Theory Archimedes' Principle states that the upward buoyant force exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces; it is also applicable to gases: 𝐹 𝑚 𝑔 There are 2 ways to measure buoyancy: direct and displacement. Direct measurement is the difference between the actual weight of the object (Wo) and its apparent weight (Wa) when fully submerged. Displacement measurement utilizes the fact that the volume of fluid displaced (Vf) is equal to the volume of the object (Vo) that is submerged. Recall that density (ρ) = m/V, such that: 𝐹 𝜌 𝑉 𝑔 𝜌 𝑉 𝑔 From the free body diagram: 𝐹 𝐹 𝑔 𝜌 𝑉 𝑚 𝑚 𝑎 where, solving for acceleration we find 𝑎 𝑔 𝜌 𝜌 1 where it can be observed that rev 01/2020 2 𝜌 𝜌 ⇒ 𝑎 𝑂𝑏𝑗𝑒𝑐𝑡 𝑤𝑖𝑙𝑙 𝑓𝑙𝑜𝑎𝑡 𝜌 𝜌 ⇒ 𝑎 0 𝑂𝑏𝑗𝑒𝑐𝑡 𝑖𝑠 𝑖𝑛 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝜌 𝜌 ⇒ 𝑎 𝑂𝑏𝑗𝑒𝑐𝑡 𝑤𝑖𝑙𝑙 𝑠𝑖𝑛𝑘 If the object is only partially submerged, then the volume of fluid displaced is the volume of the part of the object actually submerged. For example, a cylinder has a volume Vc = πr2l = Acl, where Ac = πr2 is the cross sectional area and l is the length. Assume the cylinder is submerged by a depth d, then Vsub = Acd such that: 𝐹 𝜌 𝑔𝑉 𝜌 𝑔𝐴 𝑑 It is important to note that the buoyant force and depth of the object are directly related such that buoyant force will increase with depth until the object is fully submerged. Setup Part 1 1. Fill up your graduated cylinder with enough water such that your wooden cylinder sample will float in it without touching the bottom of the graduated cylinder. (Around the 170 ml mark should do.) Procedure Part 1 1. Measure the length and diameter of your wooden cylinder sample, then record those values in the provided table. 2. Using a mass scale, measure the mass of your wooden cylinder sample, then record it in the provided table. 3. Before you place your wooden cylinder sample in the water, measure the volume of what is in your graduated cylinder and record it in the table provided as the initial volume, 𝑉 . 4. Place your wooden cylinder sample in the water, then measure the new volume, and record that volume 𝑉 in the table provided. Setup Part 2 1. Using the Vernier caliper, measure the diameter and length of each of the cylinder masses, and then record the values in the provided table. 2. Using the listed equipment, construct the setup shown in the provided picture. It doesn’t matter which cylinder mass is being used. Make sure the hook of the force sensor is pointing straight down or the sensor won’t measure all the force being applied to it. 5 Analysis of Archimedes’ Principle Lab Name______________________________________________ Group#________ Course/Section_______________________________________ Instructor____________________________________________ Table Part 1 Wooden Cylinder Values Mass (kg) Weight (N) Length (m) Diameter (m) Radius (m) Volume (m3) Density (kg/m3) Water Values Density (kg/m3) 1000 kg/m3 𝑉 (m3) 𝑉 (m3) ∆𝑉 (m3) Weight of displaced water (N) Complete Table, show any calculations in the space provided (10 points) 6 1. Draw a free body diagram of the wooden cylinder floating in the water, then write the force summation equation from that free body diagram. (Ignore if the wooden cylinder is touching the top of the graduated cylinder.) (10 points) 2. The weight of a floating object should be equal to the weight of the fluid it displaces. Calculate the % difference between the weight of your wooden cylinder, and the weight of the water it displaced when floating. Besides some small experimental error, does your result agree with the theory? If not, give some reasons why is doesn’t. (5 points) 7 Table Part 2 (Accepted Density of Water 1000 kg/m3) Brass Cylinder Values Weight (N) Length (m) Diameter (m) Radius (m) Volume (m3) WA (N) Aluminum Cylinder Values Weight (N) Length (m) Diameter (m) Radius (m) Volume (m3) WA (N) Complete Table, show any calculations in the space provided (10 points)