Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 19

Two blocks of the same density are completely submerged in water. One block has a mass equal to \(m\) and volume equal to \(V\). The other has a mass equal to \(2 m\). What is the ratio of the first block's apparent weight to the second block's apparent weight? 1\. \(1: 1\) 2\. \(1: 2\) 3\. \(2: 1\) \(\begin{array}{lll}\text { 4. } & 4: 1\end{array}\)

Short Answer

Expert verified
The ratio of the first block's apparent weight to the second block's apparent weight is 1:2.

Step by step solution

01

Find the Density of Blocks

Since both blocks have the same density, let's denote the density as 'ρ'. Using mass and volume, we can write: \[\rho = \frac{m}{V}\]
02

Volume of the Second Block

Since the two blocks have the same density and the second block has double the mass of the first block, we can find the volume of the second block: \[\rho = \frac{2m}{V_2}\] Now from Step 1, substitute the value of density: \[\frac{m}{V} = \frac{2m}{V_2}\] Solving for the volume of the second block: \[V_2 = 2V\]
03

Calculate Buoyant Forces

The buoyant force experienced by each block can be found using Archimedes' principle, which states that the upward buoyant force experienced by a submerged object is equal to the weight of the fluid it displaces. This can be written as: \[F_b = \rho_{water} \cdot V \cdot g\] For the first block, the buoyant force is: \[F_{b1} = \rho_{water} \cdot V \cdot g\] For the second block, using the volume from Step 2: \[F_{b2} = \rho_{water} \cdot 2V \cdot g\]
04

Calculate Apparent Weights

Apparent weight is the difference between an object's actual weight and the buoyant force acting on it. Let's find the apparent weights of both blocks. For the first block: \[W_{a1} = m \cdot g - F_{b1}\] For the second block: \[W_{a2} = 2m \cdot g - F_{b2}\]
05

Calculate the Ratio Apparent Weights

Now, we need to find the ratio of apparent weights of the first block to the second block: \[\frac{W_{a1}}{W_{a2}}\] Using the expressions for apparent weights from Step 4: \[\frac{m \cdot g - F_{b1}}{2m \cdot g - F_{b2}}\] Using the buoyant forces from Step 3: \[\frac{m \cdot g - \rho_{water} \cdot V \cdot g}{2m \cdot g - \rho_{water} \cdot 2V \cdot g}\] Factor out common terms: \[\frac{m( g - \rho_{water} \cdot V \cdot g)}{2m( g - \rho_{water} \cdot V \cdot g)}\] Simplifying the expression: \[\frac{m}{2m} = \frac{1}{2}\] The ratio of the first block's apparent weight to the second block's apparent weight is 1:2, which corresponds to answer choice 2.

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

What would a manufacturer of fluorescent lamps have to do in order to change his "warm white" lamps to "cool white" lamps? 1\. Change the amount of mercury vapor in the lamp to produce less ultraviolet light. 2\. Change the thickness of the glass tube to get a greater index of refraction. 3\. Change the composition of the electrodes to produce a weaker electric arc. 4\. Change the composition of the phosphor to emit more light at the blue- violet end of the spectrum.

The example given in \(\underline{\text { Table } 1}\) of a system exhibiting dipole-dipole interactions shows the molecule \(\mathrm{SO}_2\). What is the shape of this molecule? 1\. Linear 2\. Bent 3\. T-shaped 4\. Trigonal planar

Which of the following best describes the mechanism by which two substances form a maximum-boiling azeotrope? 1\. Each substance increases the specific heat of the other. 2\. Each substance decreases the specific heat of the other. 3\. Each substance increases the vapor pressure of the other. 4\. Each substance decreases the vapor pressure of the other.

A Boeing 737 aircraft has a mass of \(150,000 \mathrm{~kg}\), and a cruising velocity of \(720 \mathrm{~km} / \mathrm{hr}\). Its engines can create a total thrust of \(200,000 \mathrm{~N}\). If air resistance, change in altitude, and fuel consumption can be ignored, how long does it take for the plane to reach its cruising velocity starting from rest? 1\. \(100 \mathrm{~s}\) 2\. \(150 \mathrm{~s}\) 3\. \(540 \mathrm{~s}\) 4\. \(1944 \mathrm{~s}\)

If a cluster can be broken up by a photon with a wave number of \(1000 \mathrm{~cm}^{-1}\), what is the cluster's energy? (Note: Planck's constant \(=6.6 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\).) 1\. \(6.6 \times 10^{-31} \mathrm{~J}\) 2\. \(6.6 \times 10^{-29} \mathrm{~J}\) 3\. \(2.0 \times 10^{-26} \mathrm{~J}\) 4\. \(2.0 \times 10^{-20} \mathrm{~J}\)
See all solutions

Recommended explanations on English Textbooks

Essay Prompts

Read Explanation

English Grammar Summary

Read Explanation

Language Acquisition

Read Explanation

Rhetorical Analysis Essay

Read Explanation

International English

Read Explanation

Cues and Conventions

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