Archimedes’ Principle and Specific Density

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Physics 141 Archimedes --1

ARCHIMEDES’ PRINCIPLE AND SPECIFIC DENSITY
GOAL: To investigate buoyant force and Archimedes’ principle. To measure the specific density of several materials. INTRODUCTION: Try pushing down on a basketball in water and you feel the buoyant force that makes the ball float. As more of the ball is pushed beneath the water, the upward force becomes greater. One could make a first guess (Hypothesis #1) that the buoyant force increases with the submerged volume of the object. A more mathematical guess (Hypothesis #2) might be that the upward or buoyant force, B, is proportional to the submerged volume, Vsub, of the object. feathers, is in fact a statement that the density of lead is greater than the density of feathers. Recall for a homogeneous object with a volume, V, and a density, D, has a mass, m:

(4)
Thus the statement that lead is heavier than feathers, is correct if equal volumes of the two materials are compared. For many practical applications, it is important to be able to compare densities of various materials. One could compile a list that compares the density of everything to density of everything else, but it is easier to compare the densities of everything to just one substance, water. Water is chosen because it is very readily available and is frequently used in the measurement of density. One defines for a material with a density, Dk, a specific density, sk as:

(1)
One could try to find the correct proportionality constant for eq.1. If Hypothesis #1 or 2 are true, then once an object is completely underwater the buoyant force on it will remain constant. Does this correspond to your experience? When an object is placed in a container of water, the level of the water rises. The level raises the same height as if the volume of water was increased by the submerged volume of the object, i.e the volume of water the object displaces. Although it seems obvious that the object pushes the water out of the way and the water must go somewhere, this is an idea that is easy to test. Hypothesis # 3 is: (2) Archimedes’ principle ( from Fundamentals of Physics, 3rd edition extended, Halliday &Resnick p.371, John Wiley&Sons New York, 1988) is:

(5)
where Dwater is the density of water = 1.000 g/cm3 . This simple number is no accident because in the metric system the size of the gram was based on the mass of a cubic centimeter of water. One thing that makes specific gravity useful is that it is the same, regardless of the units used for volume, mass, weight and density. PROCEDURE: Three methods of measuring the buoyant force will be used. But first just a demo experiment. Connect the golf ball and the weak spring and slowly lower the ball into the water. What is the result? In the first method, the object being studied is suspended from a spring scale, see fig.1. As the object is lowered into the water, the reading on the scale will decrease. Although this a straightforward procedure, the spring scales are not very accurate. The second method is less direct. The container of water is on a pan balance. As the object is lowered into the water, the weights on the balance will need to be readjusted to keep the balance balanced, see fig.2. The advantage of this method is that the pan balance is much more accurate than the spring scale.

A body wholly or partially immersed in a fluid will be buoyed up by a force equal to the weight of the fluid that it displaces. The buoyant force in a fluid with a density, DF, is:

(3)
The intuitive notion that lead is “heavier” than In the third method, a graduated cylinder is placed in a beaker of water. Washers are place in the

Physics 141 Archimedes --2

graduated cylinder to vary to the mass that is floating. From the mass of the floating object and it volume ( that is part of why a graduated cylinder is used) the density of water is obtained.

measuring its geometry and/or the amount of water it displaces. Determine the specific density of the...
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