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19. Fluid Mechanics
Buoyancy & Buoyant Force
11:13 minutes
Problem 13.36
Textbook Question
Textbook Question(II) A 0.48-kg piece of wood floats in water but is found to sink in alcohol (SG = 0.79) , in which it has an apparent mass of 0.047 kg. What is the SG of the wood?
Verified step by step guidance
1
Determine the actual mass of the wood, which is given as 0.48 kg.
Calculate the buoyant force in water using the formula: Buoyant Force = Actual mass of wood - Apparent mass in water. Since the wood floats in water, its apparent mass in water is 0 kg.
Use the density of water (1000 kg/m^3) and the specific gravity of alcohol to find the density of alcohol. The formula for density of alcohol is: Density of alcohol = Specific Gravity of alcohol x Density of water.
Calculate the volume of the wood using the buoyant force in alcohol. The formula is: Volume of wood = (Actual mass of wood - Apparent mass in alcohol) / Density of alcohol.
Finally, find the specific gravity of the wood using the formula: Specific Gravity of wood = Density of wood / Density of water. Density of wood can be calculated as: Density of wood = Mass of wood / Volume of wood.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Specific Gravity (SG)
Specific Gravity (SG) is a dimensionless quantity that compares the density of a substance to the density of a reference substance, typically water for liquids. It is calculated as the ratio of the density of the substance to the density of water (1 g/cm³ at 4°C). An SG less than 1 indicates that the substance will float in water, while an SG greater than 1 means it will sink.
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Buoyancy
Buoyancy is the upward force exerted by a fluid on an object submerged in it, which counteracts the weight of the object. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object. This principle explains why objects float or sink in different fluids based on their densities relative to the fluid.
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Apparent Weight
Apparent weight refers to the weight of an object when it is submerged in a fluid, which is less than its actual weight due to the buoyant force acting on it. The apparent weight can be calculated by subtracting the buoyant force from the object's weight. In this context, the apparent weight of the wood in alcohol helps determine its specific gravity by comparing it to the buoyant force exerted by the alcohol.
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