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Archimedes' Principle Archimedes Principle states that the upward or buoyant force on an object within a fluid is equal to the weight of the fluid that the object displaces. For a partially submerged object, you can obtain information about the relative densities of the floating object and the fluid by observing how much of the object is above and below the surface. You can also determine the size of a floating object if you know the amount that is above the surface and the relative densities. You can see the top of a floating iceberg (see figure). The density of ocean water is
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Calculus: Early Transcendental Functions (MindTap Course List)
- The Ideal Gas Law A mole of a chemical is a fixed number, like a dozen, of molecules or atoms in the case of an element of that compound. A mole of water, for example, is about 18 grams, or just over half an ounce in your kitchen. Chemists often use the mole as the measure of the amount of a chemical compound. A mole of carbon dioxide has a fixed mass, but the volume V that it occupies depends on pressure p and temperature T; greater pressure tends to compress the gas into a smaller volume, whereas increasing temperature tends to make the gas expand into a larger volume. If we measure the pressure in atmospheres 1 atm is the pressure exerted by the atmosphere at sea level, the temperature in kelvins, and the volume in liters, then the relationship is given by the ideal gas law: pV=0.082T. a. Solve the ideal gas law for the volume V. b. What is the volume of 1 mole of carbon dioxide under 3 atm of pressure at a temperature of 300 kelvins? c. Solve the ideal gas law for pressure. d. What is the pressure on 1 mole of carbon dioxide if it occupies a volume of 0.4 liter at a temperature of 350 kelvins? e. Solve the ideal gas law for temperature. f. At what temperature will 1 mole of carbon dioxide occupy a volume of 2 liters under a pressure of 0.3 atm?arrow_forwardSolve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. The frustum of a right circular cone has a larger base area of 40.0 square centimeters and a smaller base area of 19.0 square centimeters. The height is 22.0 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.arrow_forwardHookes Law Hookes Law states that the force needed to keep a spring stretched x units beyond its natural length is directly proportional to x. Here the constant of proportionality is called the spring constant. a Write Hookes Law as an equation. b If a spring has a natural length of 5 cm and a force of 30 N is required to maintain the spring stretched to a length of 9 cm, find the spring constant. c What force is needed to keep the spring stretched to a length of 11 cm?arrow_forward
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