2. This is an example of a scaling problem, in which we examine the effects of changing a parameter by taking ratios. (You should expect to encounter this type of problem frequently on homework and exams.) Suppose we have a cylindrical container A, as shown in the picture below. A A second container, B, has the same shape as A, but all of its linear measurements are larger by a factor of 1.80-that is, B is 1.80 times as tall as A, and has 1.80 times the radius of A. Answer the following questions using only appropriate scaling ratios; you should not need to assume specific numerical values for the original radius and height of the cylinder. Instead, write out the expressions you need using symbols (e.g., r for the radius), take the ratio, and cancel out as much as you can before plugging in any numbers. Express all your answers in decimal form, and show your work in each case. a) This question refers to the circumference of each container. What is the dimensionality of the circumfer- ence? (i.e., what kind of quantity is it? How can it be expressed in terms of the fundamental dimensions of length (L), mass (M), and time (T)?) How will the circumference of container B compare with that of container A-that is, what is the numerical value of the ratio CB/CA? b) What is the dimensionality of area? How many times larger is the cross-sectional area of B (i.e., the area of the base of B, denoted by SB) than the cross-sectional area SA? c) What is the dimensionality of volume? If A contains 2.50 liters of water when filled to the brim, how many liters of water will B contain when filled?
2. This is an example of a scaling problem, in which we examine the effects of changing a parameter by taking ratios. (You should expect to encounter this type of problem frequently on homework and exams.) Suppose we have a cylindrical container A, as shown in the picture below. A A second container, B, has the same shape as A, but all of its linear measurements are larger by a factor of 1.80-that is, B is 1.80 times as tall as A, and has 1.80 times the radius of A. Answer the following questions using only appropriate scaling ratios; you should not need to assume specific numerical values for the original radius and height of the cylinder. Instead, write out the expressions you need using symbols (e.g., r for the radius), take the ratio, and cancel out as much as you can before plugging in any numbers. Express all your answers in decimal form, and show your work in each case. a) This question refers to the circumference of each container. What is the dimensionality of the circumfer- ence? (i.e., what kind of quantity is it? How can it be expressed in terms of the fundamental dimensions of length (L), mass (M), and time (T)?) How will the circumference of container B compare with that of container A-that is, what is the numerical value of the ratio CB/CA? b) What is the dimensionality of area? How many times larger is the cross-sectional area of B (i.e., the area of the base of B, denoted by SB) than the cross-sectional area SA? c) What is the dimensionality of volume? If A contains 2.50 liters of water when filled to the brim, how many liters of water will B contain when filled?
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter1: Units And Measurement
Section: Chapter Questions
Problem 65P: A floating-point operation is a single arithmetic operation such as addition, subtraction,...
Related questions
Question
Part C only please
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Knowledge Booster
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
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Physics for Scientists and Engineers, Technology …
Physics
ISBN:
9781305116399
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Physics for Scientists and Engineers, Technology …
Physics
ISBN:
9781305116399
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill