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LAB #5 – ARCHIMEDES’ PRINCIPLE Date __________________________ Name __________________________ Partner __________________________ Section # __________________________ Materials • brass and aluminum weights; 100-gram weight; wooden dowel; cork ball; hydrometers; graduated cylinders; triple-beam balance; string; paper clip; glass beaker; overflow can; catch bucket; table clamp and rod; vernier calipers Objective In this lab you will use Archimedes’ Principle to measure the volumes and densities of submerged objects and the buoyant forces acting on floating and submerged objects. Archimedes’ Principle • • A submerged object displaces an amount of fluid with the same volume as the object. A floating object displaces an amount of fluid with the same weight as the object. A. Density (Record your results in Table 1.) 1. Use the triple-beam balance to measure the masses of two regular solids, A (aluminum cylinder) and B (brass cube). 2. Use the vernier calipers to measure the dimensions of these regular solids to the nearest 0.1 mm: measure length (L), width (W), height (H), and/or diameter (D), as appropriate. 3. Calculate their volumes (V): a. Aluminum Cylinder: 𝑉𝑉 = 𝜋𝜋𝐷𝐷2 𝐻𝐻 4 b. Brass Cube: 𝑉𝑉 = 𝐿𝐿𝐿𝐿𝐿𝐿 4. Use these volumes to calculate experimental densities (dexp1) of the two regular solids. (Density = Mass/Volume) P-5.1 June 22, 2021 5. Use Table 4 to look up the accepted values (dacc) for the densities of these materials; record these values in Table 1. 6. Compare the experimental densities (dexp1) with the accepted values (dacc) for these materials by calculating the percent error and recording it in Table 1. % 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = 𝑑𝑑𝑒𝑒𝑒𝑒𝑒𝑒1 − 𝑑𝑑𝑎𝑎𝑎𝑎𝑎𝑎 × 100 𝑑𝑑𝑎𝑎𝑎𝑎𝑎𝑎 Table1 Object A Object B g Mass (m) g Length (L) cm Width (W) cm Height (H) cm Diameter (D) cm Volume (V) Experimental Density 1 �𝒅𝒅𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆 = Accepted Density (dacc) 𝒎𝒎 � 𝑽𝑽 % Error cm cc cc g/cc g/cc g/cc g/cc % % PAUSE – Before proceeding, discuss this result with your lab instructor to be sure you are on the right track. B. Using the Overflow Bucket to Determine the Volume of an Object. The overflow bucket system consists of two components: the overflow bucket (a tall metal can with a cylindrical spout on the side) and a catch bucket (a smaller metal can). The procedure for using these is as follows: • • • • Be sure the catch bucket is dry. Weigh the dry catch bucket and record the mass (in grams). Position a beaker – not the catch bucket – under the spout of the overflow bucket and fill the overflow bucket until water drains out of the spout into the beaker. When water has ceased to flow out of the spout, remove the beaker and replace it with the dry catch bucket. Tie a string to the object and lower it into the overflow bucket until it is submerged, collecting the overflow water in the catch bucket. P-5.2 June 22, 2021 • • • When water has ceased to flow out of the spout, remove the catch bucket and weigh it, together with its contents. Subtract the mass of the dry catch bucket to find the mass of the overflow water. Because water has a density of 1.00 g/cc, the volume of water in cc is numerically equal to the mass of the water in grams. Empty and dry the catch bucket before the next use. Submerged Objects I (Record data in Table 2.) 1. Determine the volumes of the two regular solids using the overflow bucket and Archimedes’ Principle for submerged objects. 2. Use these volumes to calculate densities of the two regular solids. 3. Compare these densities with the accepted values for these materials and calculate the % error. Table 2 Object A Object B Object Mass (m) (from Table 1) g g Mass of Catch Bucket with Water (Mchw) g g Mass of Empty Catch Bucket (Mch) g g Mass of Overflow Water (Mw) g g Volume of Overflow Water (Vw) cc cc Volume of Object (V0) cc cc g/cc g/cc g/cc g/cc % % Experimental Density 2 �𝒅𝒅𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆 = 𝒎𝒎 � 𝑽𝑽𝟎𝟎 Accepted Density (dacc) (from Table 1) % Error 4. Which data set, Table 1 or Table 2, gave better results for each object? PAUSE – Before proceeding, discuss this result with your lab instructor to be sure you are on the right track. P-5.3 June 22, 2021 C. Submerged Objects II (Record data in Table 3.) 1. Use a string to suspend one of the regular solids below the triple-beam balance pan and immerse the object in a beaker of water; use the triple-beam balance to ‘weigh’ the regular solid as it is immersed in water. Record this ‘weight’ (mw) in grams. 2. Use the loss of weight in water to calculate the buoyant force on the regular solid (in grams). 3. Compare this value with the mass of water displaced by the regular solid (from Table 2); how do they compare? 4. How should these values compare? 5. Repeat for the other regular solid. Table 3 Object A Object B Object Mass (m) (from Table 1) g g Mass of Object in water (mw) g g g g g g g g Loss of Mass (Weight) in Water (mlw = m – mw) Buoyant Force (bf) Mass of Overflow Water (from Table 2) Comparison? Suggest some specific problems with your measurements or procedure that could introduce noticeable errors into your results for the portion of the lab completed so far. P-5.4 June 22, 2021 Table 4 Densities of Common Solids and Liquids Solids balsa wood cork poplar red oak ice glass aluminum zinc tin steel brass copper lead gold density (g/cc) 0.13 0.24 0.43 0.7 0.9 2.6 2.7 7.1 7.3 7.8 8.5 8.9 11.3 19.3 Liquids gasoline octane ether isopropanol benzene coconut oil pure water sea water acetic acid glycerin chloroform carbon tetrachloride mercury density (g/cc) 0.68 0.70 0.74 0.79 0.87 0.93 1.00 1.03 1.05 1.26 1.50 1.58 13.60 D. Submerged Objects III (Record data in Table 5.) 1. Determine the mass of a cork ball using the triple-beam balance. 2. Attach a string to the cork ball; now hook a 100-gram weight over the string and lower the weight into a beaker of water such that pulling upward on the free end of the string lowers the cork ball into the water. 3. Attach the free end of the string below the triple-beam balance pan and measure the tension in the string when the ball is submerged. 4. Calculate the buoyant force on the submerged ball as the sum of the tension and the mass of the ball. 5. Use this buoyant force to determine the volume of the cork ball. 6. Use this volume to calculate the density of the cork ball. P-5.5 June 22, 2021 7. Compare this value with the density of cork from Table 4 and determine your percent error. PAUSE – Before proceeding, discuss this result with your lab instructor to be sure you are on the right track. 8. Measure the cork ball with the vernier calipers and calculate its volume = 𝜋𝜋𝐷𝐷3 6 . 9. Use this volume to calculate the density of the cork ball. 10. Compare this value with the density of cork from Table 4 and determine your percent error. Table 5 Cork Ball Mass (m) (from triple-beam balance) g String Tension on Submerged Object (T) g Buoyant Force (𝒃𝒃𝒇𝒇 = 𝑻𝑻 + 𝒎𝒎) g Volume (Vbf) (from buoyant force) Density �𝒅𝒅 = 𝒎𝒎 � 𝑽𝑽𝒃𝒃𝒃𝒃 Density (from Table 4) cc g/cc g/cc % error (buoyant force method) Diameter (D) cm Volume (V) (from diameter) cc Density (𝒅𝒅 = 𝒎𝒎 ) 𝑽𝑽 % error (diameter method) g/cc % 11. Compare these two results: which method – buoyant force or diameter measurement – gave a better value for the density? P-5.6 June 22, 2021 E. Floating Objects I (Record data in Table 6.) 1. Use the hydrometers at the front of the room to measure the densities of the liquids in the three cylinders. 2. Use the table of densities (Table 4) to identify the liquid in each cylinder. Table 6 Unknown A Hydrometer Reading Density Liquid g Unknown B Unknown C g 𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐 g 𝑐𝑐𝑐𝑐 F. Floating Objects II (Record data in Table 7.) 1. Use the vernier calipers to measure the length and diameter of the wooden dowel. 2. Calculate the volume of the dowel. 𝑉𝑉 = 𝜋𝜋𝐷𝐷2 𝐿𝐿 . 4 3. Use the triple-beam balance to measure the mass of the dowel. Record your data in Table 7. 𝑚𝑚 𝑉𝑉 4. Calculate the density of the dowel. 𝑑𝑑 = . 5. Float the dowel in a narrow cylinder of water and measure the length of the dowel that is submerged. 6. Calculate the fraction of the floating dowel that was submerged. Fs = Ls/L P-5.7 June 22, 2021 Table 7 Dowel Length (L) cm Diameter (D) cm Volume (V) cc g Mass (m) Density (d) Submerged Length (Ls) Submerged Fraction (Fs) g 𝑐𝑐𝑐𝑐 cm 7. How does the submerged fraction and the density of the dowel compare? 8. How should these two values compare? P-5.8 June 22, 2021 Physics 101 P-5 Archimedes’ Principle !!! Only do Parts A, B, C and F !!! SUPPLEMENTAL DATA Equipment Used: A-1, Aluminum Cylinder Mass A-1, Brass Cube Mass A-2, Aluminum Cylinder Dimensions Diameter (D) Height (H) A-2, Brass Cube Dimensions Length (L) Width (W) Height (H) Overflow Bucket and Catch Bucket B-1 Empty/Dry Catch Bucket Mass B-1 Aluminum Cylinder Volume Water Mass Click to Play B-1 Mass of Catch Bucket with Water: Aluminum Cylinder B-1 Brass Cube Volume Water Mass Click to Play B-1 Mass of Catch Bucket with Water: Brass Cube C-1 Aluminum Cylinder Mass Click to Play C-1 “Mass of Object in Water: Aluminum Cylinder” C-5 Brass Cube Mass Click to Play C-5 “Mass of Object in Water: Brass Cube” F-1 Wooden Dowel Dimensions Length (L) F-1 Wooden D
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