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An equation we will encounter later in the semester has the form AB variables have the following dimensionality: VH, and two of the M • [AB] L3 • [H] = T LT2 Question 1 : Determine the dimensionality of V. 1 M M [V] = [AB] · H LT² L³ L4T That means V ~ MªLT¢ where a = 1, b = -4, and c= -1. The variable V depends on the parameters , y, and z, which have the following dimensionality: M [x] = L • [y] = L [2 = LT We also know that V is directly proportional to x. How does V depend on y? How does V depend on z? Question 2 Question 3 V is proportional to x, so we can write V = xy® zb, and we have to determine a and b. Plugging in the dimensions, this equation becomes M L· Lª . L4T LT Since there is only one factor of M on the left hand side, we can concluded b = 1. That leaves M Lª M L4T which means a = -4. So V is inversely proportional to y", where n is a positive number greater than 1, and V is directly proportional to z.

An equation we will encounter later in the semester has the form AB variables have the following dimensionality: VH, and two of the M • [AB] L3 • [H] = T LT2 Question 1 : Determine the dimensionality of V. 1 M M [V] = [AB] · H LT² L³ L4T That means V ~ MªLT¢ where a = 1, b = -4, and c= -1. The variable V depends on the parameters , y, and z, which have the following dimensionality: M [x] = L • [y] = L [2 = LT We also know that V is directly proportional to x. How does V depend on y? How does V depend on z? Question 2 Question 3 V is proportional to x, so we can write V = xy® zb, and we have to determine a and b. Plugging in the dimensions, this equation becomes M L· Lª . L4T LT Since there is only one factor of M on the left hand side, we can concluded b = 1. That leaves M Lª M L4T which means a = -4. So V is inversely proportional to y", where n is a positive number greater than 1, and V is directly proportional to z.

An Introduction to Physical Science
An Introduction to Physical Science
14th Edition
ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Chapter1: Measurement
Section: Chapter Questions
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I need help understanding the dimensional analysis question

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An equation we will encounter later in the semester has the form AB variables have the following dimensionality: VH, and two of the M • [AB] L3 • [H] = T LT2 Question 1 : Determine the dimensionality of V. 1 M M [V] = [AB] · H LT² L³ L4T That means V ~ MªLT¢ where a = 1, b = -4, and c= -1. The variable V depends on the parameters , y, and z, which have the following dimensionality: M [x] = L • [y] = L [2 = LT We also know that V is directly proportional to x. How does V depend on y? How does V depend on z? Question 2 Question 3 V is proportional to x, so we can write V = xy® zb, and we have to determine a and b. Plugging in the dimensions, this equation becomes M L· Lª . L4T LT Since there is only one factor of M on the left hand side, we can concluded b = 1. That leaves M Lª M L4T which means a = -4. So V is inversely proportional to y", where n is a positive number greater than 1, and V is directly proportional to z.
Transcribed Image Text:An equation we will encounter later in the semester has the form AB variables have the following dimensionality: VH, and two of the M • [AB] L3 • [H] = T LT2 Question 1 : Determine the dimensionality of V. 1 M M [V] = [AB] · H LT² L³ L4T That means V ~ MªLT¢ where a = 1, b = -4, and c= -1. The variable V depends on the parameters , y, and z, which have the following dimensionality: M [x] = L • [y] = L [2 = LT We also know that V is directly proportional to x. How does V depend on y? How does V depend on z? Question 2 Question 3 V is proportional to x, so we can write V = xy® zb, and we have to determine a and b. Plugging in the dimensions, this equation becomes M L· Lª . L4T LT Since there is only one factor of M on the left hand side, we can concluded b = 1. That leaves M Lª M L4T which means a = -4. So V is inversely proportional to y", where n is a positive number greater than 1, and V is directly proportional to z.
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