Physics Bouyant Force See the figure for the

Physics

Bouyant Force See the figure for the equation derivation: The top and bottom surface of the box are both A.

Bouyant Force The upward force on the bottom of the surface (Fb) of the “box” is: The downward force on the top of the surface (Ft) of the “box” is:

Bouyant Force The net upward force (BF) is given by:

Bouyant Force From the formula: and Substituting: Therefore: The bouyant force equals the weight of the displaced liquid.

Bouyant Force The density used in this in bouyant force called the weight density (D). This denoted by the formula:

Sample Problem A block of copper of volume 0. 5 ft 3 is immersed in ocean water. Use weight density of copper is 555 lbs/ft 3 and weight density of ocean water is 64. 4 lbs/ft 3. a. What is the weight of this block? b. What is the BF on this block? c. What force would be needed to raise this block while it is immersed in ocean water?

Sample Problem Solution: a. The weight of the block can be found by using the equation:

Sample Problem Solution: b. The BF can be found by finding the weight of 0. 5 ft 3 of displaced ocean water. Therefore BF = 32. 2 lbs.

Sample Problem Solution: c. The force needed to lift this copper block in ocean water is found by noting that the BF helps to raise the block. Therefore,

Archimedes’ Principle Applied to Bodies that Float A body will float in any liquid that has a weight density greater than the weight density of the body. The weight density of the ocean water is 64. 4 lbs/ft 3 and lake water has the weight density of 62. 4 lbs/ft 3. Bodies float either “high” or “low” depending on the weight of the block or the object. Some parts of the floating objects are underwater, some are above the water surface.

Archimedes’ Principle Applied to Bodies that Float Consider the following sample problem: A submarine thrust out a block which has a weight density of 48. 3 lbs/ft 3 and a volume of 2 ft 3 in ocean water. Obviously, the block will rise because the block has lesser weight density than water which is 64. 4 lbs/ft 3. Solving for the weight of the block:

Archimedes’ Principle Applied to Bodies that Float Ocean water is displaced at: The block will rise until the BF has been reduced to 96. 6 lbs (weight of the block).

Archimedes’ Principle Applied to Bodies that Float Solving for the ratio of the weight density of the block to the weight density of the ocean water: This means that the block is floating 75% under water. That also means BF is reduced to the weight of the block when multiplied by 0. 25.

Hydrometers It is a device used for measuring the specific gravity of liquids, such as the battery fluid in an aircraft battery. The “float” in a hydrometer floats higher or lower depending on the density of the battery fluid. The “float” is calibrated to indicate this density. Thus, there is a possibility of determining the condition of the aircraft battery.

Archimedes’ Principles as Applied to Dirigibles Archimedes Principles is not only applied to liquids but also with gases. Sample Problem: The bag of a balloon is a sphere of radius 25 m filled with hydrogen of weight density 0. 882 N/m 3. What total weight (in Newtons) of fabric, car, and contents can be lifted by this balloon in air of weight density 12. 6 N/m 3?

Archimedes’ Principles as Applied to Dirigibles Solution: Calculate the volume of the spherical balloon:

Archimedes’ Principles as Applied to Dirigibles Solution: Then calculate weight of the hydrogen. Then the weight of the displaced air, which is also equal to BF:

Exercises 1. A solid aluminum object of volume 250 ft 3 is resting on the ocean floor. A salvage crew plans to raise this object. What force will be needed? Assume aluminum D=169 lbs/ft 3. 2. What percentage of an iceberg is below the surface of the ocean? Assume iceberg D=57. 5 lbs/ft 3. 3. A rowboat and contents weighing 550 lbs is floating on Lake Michigan. What volume of water does this boat displace?