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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?

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?

University Physics Volume 1
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 1.7CYU: Check Your Understanding Figure 1.4 says the mass of the atmosphere is 1019kg . Assuming the density...
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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? CONTINUED ON NEXT PAGE
Transcribed Image Text: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? CONTINUED ON NEXT PAGE
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