Lab 8 – Archimedes' Principle and Buoyancy, Schemes and Mind Maps of Acting

Download Lab 8 – Archimedes' Principle and Buoyancy and more Schemes and Mind Maps Acting in PDF only on Docsity! Lab 8 – Archimedes’ Principle and Buoyancy Equipment  Chemical splash goggles (Students bring their own)  Distilled/Deionized Water, Isopropyl alcohol  Calculator, Computer  Set of Digital Calipers  Spring Scale or Force Sensor  Plastic bins to catch overflow.  Graduated cylinder  Aluminum Container with spout  Vertical stand, perpendicular clamp, horizontal rod (between 20 cm and 50 cm)  Brass Ball with a string attached to it  Wooden cylinder with pencil lines marking off equal lengths  Capstone setup file: Force Sensor – Digits Display.cap Objectives Verify Archimedes’ principle and use the Archimedes’ principle to determine the density of a given liquid. Introduction The famous legend tells us that Archimedes was the person who discovered that the volume of displaced water equals the volume of a submerged object. He came up with that idea as he was trying to measure the volume of a crown of unusual shape. Puzzled he had filled his bathtub flush with water and water overflowed when he got inside of the tub. The idea that the amount of water splashed out of the tub is exactly the volume of his own body struck him and he ran outside of his house crying “Eureka!” This means, “I have found it”. Archimedes’ Principle itself isn’t directly about volume, it’s about buoyancy. It states that the buoyant upward force acting on an object entirely or partially submerged in a fluid is equal to the weight of the fluid displaced by the object. For a given object, the weight can be directly calculated from the mass or from the density and volume: 𝐹𝑔 = 𝑚𝑔 = 𝜌𝑉𝑔 The buoyant force is found by applying the same idea to the fluid instead of the object: 𝐹𝐵 = 𝑚fluid𝑔 = 𝜌fluid𝑉displaced𝑔 (1) Here, 𝑚fluid is the mass of the displaced fluid, which is broken down as the density of the fluid 𝜌fluid multiplied by the submerged volume of the object 𝑉displaced. For a prism-shaped object like a cylinder, the submerged volume is equal to the cross-sectional area, 𝐴, multiplied by the submerged depth, 𝑑. So the buoyant force can be written as: 𝐹𝐵 = 𝜌fluid𝐴𝑑𝑔 (2) If the object is lowered into the fluid while the buoyant force is measured, the slope of the graph of 𝐹𝐵 versus 𝑑 is proportional to the density of the fluid. Figure 1: Schematic picture for the experiment Part I. Verifying Archimedes Principle Figure 2. Ready to perform Experiment 1. Read the instructions below; this picture is just so you have an idea of what is going on. The upper container (with the spout) was set in place, and then it was “topped off” with water. (The extra water fell into the plastic bin.) The graduated cylinder is ready to catch the overflow that will come out when the brass ball is lowered into the water. (Do not copy our picture into your lab report!) Figure 3. Taking data for Experiment 3. The cup of water has been brought up under the mass until it reached the desired line. The tension recorded by the spring scale is not the weight of the block, as it has been reduced by the buoyancy force. (Do not copy our picture into your lab report!) DATA RECORDING: 1. Hang the wooden block from the Force Sensor and display the reading as with the sphere. 2. Take a reading of the block’s weight when measured in air (𝐹𝑇 = 𝐹𝑔). Note that 𝐹𝑔 doesn’t change throughout the experiment. 3. Submerge the wooden block suspended from the force sensor down in water to the first pencil mark (1cm depth) and record its “weight in water” (𝐹𝑇, which is not 𝐹𝑔). You can lower the block into the water or raise the water under the block; it doesn’t matter which. 4. Repeat the same procedure for each mark until the wooden cylinder starts floating. 5. Once the block starts actually floating, or if the block leans against the side of the container, don’t any more data. 6. Record your experimental data in a table similar to Table 3. ANALYZING THE DATA: 1. Calculate the buoyant force (𝐹𝐵 = 𝐹𝑔 − 𝐹𝑇) for each data point. 2. Plot the buoyant force 𝐹𝐵 versus the submerged depth, 𝑑. 3. Determine the slope of the graph and compute the density of the liquid. Record this in something similar to Table 4. 7. Calculate the % Difference between the accepted value (1,000 kg/m3) for the density of water and the value you found from the slope. Depth 𝒅 (m) 𝑭𝒈 (N) 𝑭𝑻 (N) 𝑭𝑩 (N) Table 3: Replace this text with an appropriate caption. Slope of 𝐹𝐵 vs. 𝑑 (N/m) Density of liquid, 𝜌 (kg/m³) Expected 𝜌 (kg/m³) % Error Table 4. Replace this text with an appropriate caption. Experiment 4. Density of isopropyl alcohol  Wear chemical safety goggles. If you get isopropyl alcohol in your eye, go to the eyewash station and flush it out.  Don’t drink the isopropyl alcohol; it’s poisonous not drinkable.  If you get isopropyl alcohol on your skin, dry it off. Isopropyl alcohol is also known as rubbing alcohol and getting a small amount on your skin shouldn’t harm you.  Don’t spill the alcohol.  Ask the instructor about waste collection. Repeat Experiment 3, but using isopropyl alcohol as the fluid instead of water. Make data tables and a graph.