bartleby

Concept explainers

Question
Chapter 14, Problem 1CQ
To determine

Whether the object’s density change and by what factor.

Expert Solution & Answer
Check Mark

Answer to Problem 1CQ

Solution: (a) The density ρremains constant. (b) The density decreases by a factor of 8.

Explanation of Solution

Given:

An object has density ρ . (a) Each of the objects 3 dimensions is increased by a factor of 2 without changing the material of which the object is made. (b) The dimensions are increased by a factor of 2 without changing the object’s mass.

Formula used:

The mass of an object with uniform density ρ is given by m=ρV , where V volume of the object.

(a) When the volume increases, the mass also proportionally increases. Since the object’s material does not change, the density ρ remains constant. (b) Since, the linear dimensions change by a factor of 2, the density decreases by a factor of 8.

Calculation:

The mass remains constant. Hence, m=ρV=ρ'V' . Now, since the linear dimensions change by a factor of 2, new volume V' is 2×2×2V=8V .

Substituting,

m=ρV=ρ'(8V)ρ'=ρ8

Conclusion:

Since the object’s material does not change, the density ρ remains constant. Since, the linear dimensions change by a factor of 2, the density decreases by a factor of 8.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 14 Solutions

Modified Mastering Physics with Pearson eText -- Standalone Access Card -- for Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Ch. 14 - Prob. 11CQCh. 14 - Prob. 12CQCh. 14 - Prob. 13CQCh. 14 - What is the volume in mL of 55 g of a liquid with...Ch. 14 - Prob. 2EAPCh. 14 - Prob. 3EAPCh. 14 - A 6.0m12.0m swimming pool slopes linearly from a...Ch. 14 - A 1.0-m-diameter vat of liquid is 2.0 m deep. The...Ch. 14 - Prob. 6EAPCh. 14 - A 3.0-cm-diameter tube is held upright and filled...Ch. 14 - a. What volume of water has the same mass as 8.om3...Ch. 14 - A 50-cm-thick layer of oil floats on a...Ch. 14 - A research submarine has a 20-cm-diameter window...Ch. 14 - A 20-cm-diameter circular cover is placed over a...Ch. 14 - Prob. 12EAPCh. 14 - Prob. 13EAPCh. 14 - Prob. 14EAPCh. 14 - 15. How far must a 2.0-cm-diameter piston be...Ch. 14 - A 6.00-cm-diameter sphere with a mass of 89.3 g is...Ch. 14 - Prob. 17EAPCh. 14 - Prob. 18EAPCh. 14 - Prob. 19EAPCh. 14 - Prob. 20EAPCh. 14 - What is the tension of the string in FIGURE...Ch. 14 - 22. A 10-cm-diameter, 20-cm-tall steel cylinder (=...Ch. 14 - You need to determine the density of a ceramic...Ch. 14 - Prob. 24EAPCh. 14 - Prob. 25EAPCh. 14 - Prob. 26EAPCh. 14 - A long horizontal tube has a square cross section...Ch. 14 - Prob. 28EAPCh. 14 - Prob. 29EAPCh. 14 - Prob. 30EAPCh. 14 - A 2.0 mL syringe has an inner diameter of 6.0 mm,...Ch. 14 - Prob. 32EAPCh. 14 - Prob. 33EAPCh. 14 - Prob. 34EAPCh. 14 - Prob. 35EAPCh. 14 - Prob. 36EAPCh. 14 - Prob. 37EAPCh. 14 - Prob. 38EAPCh. 14 - Prob. 39EAPCh. 14 - Prob. 40EAPCh. 14 - 41. A friend asks you how much pressure is in your...Ch. 14 - Prob. 42EAPCh. 14 - Prob. 43EAPCh. 14 - 44. A U-shaped tube, open to the air on both ends,...Ch. 14 - Prob. 45EAPCh. 14 - Prob. 46EAPCh. 14 - An aquarium of length L, width (front to back) W,...Ch. 14 - Prob. 48EAPCh. 14 - Prob. 49EAPCh. 14 - 50. A cylinder with cross-section area A floats...Ch. 14 - Prob. 51EAPCh. 14 - Prob. 52EAPCh. 14 - Prob. 53EAPCh. 14 - Prob. 54EAPCh. 14 - A plastic "boat" with a square cross section...Ch. 14 - Prob. 56EAPCh. 14 - Prob. 57EAPCh. 14 - Prob. 58EAPCh. 14 - Prob. 59EAPCh. 14 - Prob. 60EAPCh. 14 - Prob. 61EAPCh. 14 - Prob. 62EAPCh. 14 - Prob. 63EAPCh. 14 - Prob. 64EAPCh. 14 - A hurricane wind blows across a 6.0m15.0m flat...Ch. 14 - Prob. 66EAPCh. 14 - Prob. 67EAPCh. 14 - A water tank of height h has a small hole at...Ch. 14 - Prob. 69EAPCh. 14 - Prob. 70EAPCh. 14 - 71. The bottom of a steel "boat" is a piece . The...Ch. 14 - Prob. 72EAPCh. 14 - Prob. 73EAPCh. 14 - Prob. 74EAPCh. 14 - Prob. 75EAP
Knowledge Booster
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • College Physics
    Physics
    ISBN:9781305952300
    Author:Raymond A. Serway, Chris Vuille
    Publisher:Cengage Learning
    University Physics (14th Edition)
    Physics
    ISBN:9780133969290
    Author:Hugh D. Young, Roger A. Freedman
    Publisher:PEARSON
    Introduction To Quantum Mechanics
    Physics
    ISBN:9781107189638
    Author:Griffiths, David J., Schroeter, Darrell F.
    Publisher:Cambridge University Press
  • Physics for Scientists and Engineers
    Physics
    ISBN:9781337553278
    Author:Raymond A. Serway, John W. Jewett
    Publisher:Cengage Learning
    Lecture- Tutorials for Introductory Astronomy
    Physics
    ISBN:9780321820464
    Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
    Publisher:Addison-Wesley
    College Physics: A Strategic Approach (4th Editio...
    Physics
    ISBN:9780134609034
    Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
    Publisher:PEARSON
  • College Physics
    Physics
    ISBN:9781305952300
    Author:Raymond A. Serway, Chris Vuille
    Publisher:Cengage Learning
    University Physics (14th Edition)
    Physics
    ISBN:9780133969290
    Author:Hugh D. Young, Roger A. Freedman
    Publisher:PEARSON
    Introduction To Quantum Mechanics
    Physics
    ISBN:9781107189638
    Author:Griffiths, David J., Schroeter, Darrell F.
    Publisher:Cambridge University Press
    Physics for Scientists and Engineers
    Physics
    ISBN:9781337553278
    Author:Raymond A. Serway, John W. Jewett
    Publisher:Cengage Learning
    Lecture- Tutorials for Introductory Astronomy
    Physics
    ISBN:9780321820464
    Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
    Publisher:Addison-Wesley
    College Physics: A Strategic Approach (4th Editio...
    Physics
    ISBN:9780134609034
    Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
    Publisher:PEARSON