Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 35

An aluminum cylinder weighs \(1.03 \mathrm{N}\). When this same cylinder is completely submerged in alcohol, the volume of the displaced alcohol is $3.90 \times 10^{-5} \mathrm{m}^{3} .$ If the cylinder is suspended from a scale while submerged in the alcohol, the scale reading is \(0.730 \mathrm{N}\). What is the specific gravity of the alcohol? (tutorial: ball in beaker).

Short Answer

Expert verified
Answer: The specific gravity of the alcohol is approximately 0.7846.

Step by step solution

01

Understand Archimedes' Principle

Archimedes' Principle states that the buoyant force (upward force) on a submerged object is equal to the weight of the fluid displaced by that object. In this case, the fluid is the alcohol, and the object is the aluminum cylinder.
02

Calculate the buoyant force

The buoyant force can be calculated as the difference between the weight of the cylinder in air and the weight of the cylinder when it is submerged in alcohol. Buoyant force (\(F_B\)) = Weight in air - Submerged weight = \(1.03 \mathrm{N}\) - \(0.730 \mathrm{N}\) = \(0.300 \mathrm{N}\)
03

Find the weight of the displaced alcohol

The buoyant force is equal to the weight of the fluid displaced, so the weight of the displaced alcohol is also \(0.300 \mathrm{N}\).
04

Calculate the mass of the displaced alcohol

To calculate the mass of the displaced alcohol, we can use the formula: weight = mass × acceleration due to gravity (\(g\)). In this case, we know the weight of the displaced alcohol (\(0.300 \mathrm{N}\)) and the acceleration due to gravity (\(9.81 \mathrm{m/s^2}\)). Mass of the displaced alcohol = \(\frac{Weight}{g}\) = \(\frac{0.300 \mathrm{N}}{9.81 \mathrm{m/s^2}}\) = \(0.0306 \mathrm{kg}\)
05

Calculate the density of the alcohol

To find the density of the alcohol, we will use the formula: density = \(\frac{mass}{volume}\). We are given the volume of the displaced alcohol as \(3.90 \times 10^{-5} \mathrm{m}^{3}\), and we have found the mass of the displaced alcohol (\(0.0306 \mathrm{kg}\)). Density of the alcohol = \(\frac{0.0306 \mathrm{kg}}{3.90 \times 10^{-5} \mathrm{m}^{3}}\) = \(784.62 \mathrm{kg/m^3}\)
06

Find the specific gravity of the alcohol

Specific gravity is a ratio of the density of a fluid to the density of a standard reference fluid (usually water). Specific gravity is a unitless quantity, and for water, specific gravity = 1. The density of water is approximately \(1000 \mathrm{kg/m^3}\). Specific gravity of the alcohol = \(\frac{Density \ of \ alcohol}{Density \ of \ water}\) = \(\frac{784.62 \ \mathrm{kg/m^3}}{1000 \ \mathrm{kg/m^3}}\) = \(0.7846\) The specific gravity of the alcohol is approximately 0.7846.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A bug from South America known as Rhodnius prolixus extracts the blood of animals. Suppose Rhodnius prolixus extracts \(0.30 \mathrm{cm}^{3}\) of blood in 25 min from a human arm through its feeding tube of length \(0.20 \mathrm{mm}\) and radius \(5.0 \mu \mathrm{m} .\) What is the absolute pressure at the bug's end of the feeding tube if the absolute pressure at the other end (in the human arm) is 105 kPa? Assume the viscosity of blood is 0.0013 Pa-s. [Note: Negative absolute pressures are possible in liquids in very slender tubes.]
If you watch water falling from a faucet, you will notice that the flow decreases in radius as the water falls. This can be explained by the equation of continuity, since the cross-sectional area of the water decreases as the speed increases. If the water flows with an initial velocity of $0.62 \mathrm{m} / \mathrm{s}\( and a diameter of \)2.2 \mathrm{cm}$ at the faucet opening, what is the diameter of the water flow after the water has fallen $30 \mathrm{cm} ?$
An airplane flies on a level path. There is a pressure difference of 500 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about \(100 \mathrm{m}^{2} .\) The air moves below the wings at a speed of \(80.5 \mathrm{m} / \mathrm{s} .\) Estimate (a) the weight of the plane and (b) the air speed above the wings.
Water entering a house flows with a speed of \(0.20 \mathrm{m} / \mathrm{s}\) through a pipe of \(1.0 \mathrm{cm}\) inside radius. What is the speed of the water at a point where the pipe tapers to a radius of \(2.5 \mathrm{mm} ?\)
Use Bernoulli's equation to estimate the upward force on an airplane's wing if the average flow speed of air is \(190 \mathrm{m} / \mathrm{s}\) above the wing and \(160 \mathrm{m} / \mathrm{s}\) below the wing. The density of the air is \(1.3 \mathrm{kg} / \mathrm{m}^{3}\) and the area of each wing surface is $28 \mathrm{m}^{2}$
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Astrophysics

Read Explanation

Force

Read Explanation

Electricity

Read Explanation

Nuclear Physics

Read Explanation

Modern Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free