Archimedes' Principle, Buoyancy, and Density, Exams of Acting

Download Archimedes' Principle, Buoyancy, and Density and more Exams Acting in PDF only on Docsity! Archimedes’ Principle, Buoyancy, and Density Equipment • Chemical splash goggles (Students bring their own) • Distilled/Deionized Water, Isopropyl alcohol • Computer with a spreadsheet software • Set of Digital Calipers • Force Sensor • Plastic bins to catch overflow. • Graduated cylinder • Aluminum Container with and without spout • Vertical stand, perpendicular clamp, horizontal rod (between 20 cm and 50 cm) • Metal Ball with a string attached to it • Wooden cylinder with pencil lines marking off equal lengths Objectives • Verify Archimedes’ principle and use it 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. Part 1. Volume of the Displaced Liquid The purpose of this experiment is to verify Archimedes’ “finding” that the volume of the displaced liquid is the same as the volume of the object immersed. A metal ball will be used as the solid object. 1. Find the volume of the ball by measuring its diameter and using that to calculate the volume of the ball, assuming that it is a perfect sphere. 2. Submerge the ball in water and determine the volume of the water displaced. (See Figure 1.) • Place the aluminum container (the one with a spout) in position where you can catch any overflow with the graduated cylinder. • Fill the container with water so it just overflows (don’t catch this water), then allow it to stop dripping. Note that if you move the container after it’s full, you’ll slosh some water out, so get the container fixed in position first, then fill it. • Prepare to catch any additional water that comes out of the spout with the graduated cylinder. • Lower the ball in the water while catching the overflow in the graduated cylinder. Figure 1. Ready to perform Part 1. 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!) 10. Repeat 2-9 but using isopropyl alcohol as the fluid instead of water. Label data tables for this part as 3a and 4a. Have a similar approach to the graph labeling. Depth 𝒅 (m) 𝑭𝒈 (N) 𝑭𝑻,water (N) 𝑭𝑩 (N) 0.01 0.02 0.03 … Table 3: Replace this text with an appropriate caption. Slope of 𝐹𝐵 vs. 𝑑 (N/m) Area of base of block (m^2) Density of liquid, 𝜌 (kg/m³) Expected 𝜌 (kg/m³) % Error Table 4. Replace this text with an appropriate caption. • Wear chemical safety goggles when alcohol is being used. 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. Requirements for the Lab 8 Formal Report (also consult the rubric): Save your Excel files through your Blackboard Group File Exchange. • The Abstract should be written last BUT be at the front of the report • The Main Body of the report must address the following o The introductory should have a background information about the nature of buoyant force and how it is reflected in Archimedes Principle. o The methods should explain: 1. How the data was collected and calculated for Table 1 (what tool was used to measure the diameter of the ball and how this measurement was used for the calculation of the volume of the ball; how the displaced water was collected, and the volume of the displaced water was calculated). 2. How the data was collected and calculated for Table 2 (what tool was used to measure the weight of the ball in the air/water and how the buoyant force was computed from these measured values; explain what was measured to compute the weight of the displaced water and how these measurements were done) 3. How the data was collected and calculated for Tables 3 and 3a including a comment on how the manipulation of the submerged depth was reflected in the measured values of the buoyant force. 4. How the data from Tables 3 and 3a was analyzed including interpretation of the trendlines (how the slope of the graph was used to calculate the value of the density) o The discussion should quantitatively present how well the data from Table 1 and 2 supports Archimedes Principle (state what was expected and if it was achieved) and use tables 4 and 4a to discuss how Archimedes Principle was used in calculations of densities (quantitatively compare the experimental and accepted values of the densities). • The data section must include: o 6 Tables (labeled and captioned) o 2 Graphs (titled, axis labels, units, labeled and captioned)