Textbook Question
A 2.0 cm ✕ 2.0 cm ✕ 6.0 cm block floats in water with its long axis vertical. The length of the block above water is 2.0 cm. What is the block's mass density?
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Ch 14: Fluids and Elasticity
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 14, Problem 14
What is the minimum hose diameter of an ideal vacuum cleaner that could lift a 10 kg (22 lb) dog off the floor?
Verified step by step guidance1
Identify the force needed to lift the dog. This is done by calculating the weight of the dog using the formula F = mg, where m is the mass of the dog and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Determine the pressure difference required to lift the dog. Since the force exerted by the vacuum cleaner is due to the pressure difference between the atmospheric pressure and the pressure inside the vacuum, use the formula F = A \(\Delta\) P, where A is the cross-sectional area of the hose and \(\Delta\) P is the pressure difference.
Rearrange the formula to solve for the cross-sectional area A of the hose: A = F / \(\Delta\) P. Here, \(\Delta\) P can be assumed to be close to the atmospheric pressure (about 101,325 Pa) since the pressure inside an ideal vacuum cleaner can approach zero.
Calculate the diameter of the hose from the area. The area of a circle (which is the cross-section of the hose) is given by A = \(\pi\) (d/2)^2, where d is the diameter of the hose. Solve for d: d = 2 \(\sqrt{A / \pi}\).
Consider practical adjustments and safety factors, such as ensuring the diameter calculated is feasible for a vacuum cleaner and checking if the suction can be achieved without harming the dog.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Vacuum Pressure
Vacuum pressure refers to the pressure difference created by a vacuum cleaner, which generates suction. It is the difference between atmospheric pressure and the pressure inside the vacuum cleaner's hose. To lift an object, the vacuum pressure must be sufficient to overcome the weight of the object, which can be calculated using the formula: Pressure = Force/Area.
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Force and Weight
Force is a vector quantity that causes an object to accelerate, while weight is the force exerted by gravity on an object. The weight of an object can be calculated using the formula: Weight = mass × gravitational acceleration (approximately 9.81 m/s² on Earth). For a 10 kg dog, the weight would be 98.1 N, which is the force that the vacuum must counteract to lift the dog.
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Hose Diameter and Flow Rate
The diameter of the hose affects the flow rate of air and the vacuum cleaner's ability to create suction. A larger diameter allows for more air to flow, which can reduce the vacuum pressure, while a smaller diameter increases the velocity of the air, enhancing suction. The relationship between hose diameter, flow rate, and vacuum pressure is crucial for determining the minimum diameter needed to lift a specific weight.
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Related Practice
Textbook Question
What is the tension of the string in FIGURE EX14.19?
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Textbook Question
The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. What is the pressure difference between points 1 and 2? Between points 1 and 3?
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Textbook Question
The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. What is the pressure at point 1?
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Textbook Question
What is the height of a water barometer at atmospheric pressure?
Textbook Question
A 6.00-cm-diameter sphere with a mass of 89.3 g is neutrally buoyant in a liquid. Identify the liquid.
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