Answer Happy

Dimensions Length (cm) Height (cm) Diameter (cm) Radius (cm) 1 Calculated Volume (cm³) 2 3 Density (Method 1) in g/cm² 4 pm/V 15 16 Apparent mass, m' in grams, 17 when submerged in water 18 19 Density (Method 2) in g/cm³ 20 Calculated from Eq (6) 21 22 % Difference in density 23 between Methods 1 & 2 24 25 % Difference between. 26 Accepted Density of Al 27 and Method 2 28 7.27 2.53 1.27 66.0 3.16 55.4 Accepted Density of Aluminum 2.70 g/cm³
Introduction: The mass density of an object is one of its more basic physical properties and is defined: Eq (1) m V The average density of an object can be found simply by measuring the object's mass, m, and dividing this by its calculated volume, V. In SI unit's density is expressed in kg/m³. In this experiment we will use the more convenient units of grams per cubic centimeter g/cm³. Another method for finding the density employs Archimedes Principle of buoyancy. His principle states that any object immersed in a fluid will experience an upward buoyant force. Furthermore, this buoyant force has a magnitude equal to the weight of fluid the object displaces. Consider what would happen if the beaker of fluid shown in Figure 1 were removed. The block, shown in the diagram, would then be hanging in air by the thread which is attached below the balance. The block's mass, and therefore its weight, would be the same as if it were simply placed on the scale pan and "weighed", or more correctly "massed". When suspended below the balance the tension in the thread balances the force of gravity, or weight of the object. The object's weight and mass are related by the equation. W = mg Eq (2) where g is the acceleration of gravity, 9.8 m/s². The electronic balance could be calibrated to measure this force, (weight) in SI units of Newtons. However, like most balances, this balance is calibrated to read the object's mass, m, in grams, not its weight. As equation (2) clearly shows, weight and mass are distinctly different quantities. If an object is fully immersed in a fluid, as shown in Figure 1, the electronic balance will respond to the change in the tension in the thread. In this case this tension is equal to the weight, W, minus the upward buoyant force, FB, of the fluid. This tension is called the apparent weight, of the submerged object, W'. The balance will read the apparent mass, m', not the true mass of the object. The quantities are related by the expression: W' = m'g = mg - FB Eq (3)
where g is the acceleration of gravity, 9.8 m/s². The electronic balance could be calibrated to measure this force, (weight) in SI units of Newtons. However, like most balances, this balance is calibrated to read the object's mass, m, in grams, not its weight. As equation (2) clearly shows, weight and mass are distinctly different quantities. If an object is fully immersed in a fluid, as shown in Figure 1, the electronic balance will respond to the change in the tension in the thread. In this case this tension is equal to the weight, W, minus the upward buoyant force, FB, of the fluid. This tension is called the apparent weight, of the submerged object, W'. The balance will read the apparent mass, m', not the true mass of the object. The quantities are related by the expression: W' = m'g = mg - FB Eq (3) From Archimedes' Principle the buoyant force, Fa, is equal to the weight of the fluid displaced. If me is used to denote the mass of the fluid displaced, Vethe volume, and pr the density of the fluid, then the buoyant force can be expressed as: Eq (4) FB = mfg = PfVf9 = PfVg We have used the fact that the mass of the fluid displaced equals the density of the fluid times the volume of the fluid displaced and, the fact that when the object is fully submerged the volume of the fluid displaced is the same as the volume of the object. Substituting Fa in Eq (4) into Eq (3) and using the fact that V = m/p, Eq (3) becomes: PL mg m'g = mg P Some simple algebra can be used to rearrange the expression to give: mp f m-m' Eq (5) Eq (6)
1 Density of Water (g/cm³) 2 3 Quantity 4 Mass (g) 5 6 Dimensions 7 Length (cm) 8 Height (cm) 9 Diameter (cm) 10 Radius (cm) 11 Calculated Volume (cm³) 12 13 Density (Method 1) in g/cm³ 14 p= m/V 15 16 Apparent mass, m' in grams, 17 when submerged in water 18 19 Density (Method 2) in g/cm³ 20 Calculated from Eq (6) 21 22 % Difference in density 23 between Methods 1 & 2 24 25 % Difference between 1.00 Metal Cylinder 104 7.27 2.53 1.27 66.0 Metal Block 87.4 3.16 55.4 Accepted Density of Aluminum 2.70 g/cm