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Ch 12: Fluid Mechanics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 12: Fluid MechanicsProblema 29
Capitolo 12, Problema 29

An ore sample weighs 17.50 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.20 N. Find the total volume and the density of the sample.

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First, understand that the weight of the ore sample in air (17.50 N) is the gravitational force acting on it, which can be expressed as \( F_{\text{gravity}} = mg \), where \( m \) is the mass and \( g \) is the acceleration due to gravity (approximately 9.81 m/s²).
Next, recognize that when the sample is immersed in water, it experiences a buoyant force. The tension in the cord (11.20 N) is the apparent weight of the sample in water. The buoyant force can be calculated using the equation \( F_{\text{buoyant}} = F_{\text{gravity}} - F_{\text{tension}} \).
The buoyant force is also equal to the weight of the water displaced by the sample, which can be expressed as \( F_{\text{buoyant}} = \rho_{\text{water}} V g \), where \( \rho_{\text{water}} \) is the density of water (approximately 1000 kg/m³) and \( V \) is the volume of the sample. Use this equation to solve for the volume \( V \).
Once the volume \( V \) is found, calculate the mass of the sample using its weight in air: \( m = \frac{F_{\text{gravity}}}{g} \).
Finally, determine the density of the sample using the formula \( \rho = \frac{m}{V} \), where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume of the sample.

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Concetti chiave

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Buoyancy

Buoyancy is the upward force exerted by a fluid on an object submerged in it. This force is equal to the weight of the fluid displaced by the object. In this problem, the difference in weight of the ore sample in air and in water is due to the buoyant force acting on it, which helps in determining the volume of the sample.
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Percorso guidato
11:06
Intro to Buoyancy & Buoyant Force

Archimedes' Principle

Archimedes' Principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. This principle is crucial for calculating the volume of the ore sample, as the difference in tension when the sample is submerged provides the weight of the displaced water.
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14:47
Diffraction with Huygen's Principle

Density

Density is defined as mass per unit volume and is a measure of how much matter is packed into a given space. To find the density of the ore sample, we need to calculate its mass from the weight in air and then divide it by the volume obtained using the buoyant force. This will give us the sample's density, which is a key property in material identification.
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Percorso guidato
8:13
Intro to Density
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