The maximum running speed (S) in km/hr and the corresponding body mass (m) in kg were determined for 55 different species of mammals. An empirical relation was determined to be: S[km/hr] = 5.7 (m[kg])2 . Note: The notation in this equation means, “inserting the mass (m) in units of ‘kg’, automatically calculates the maximum running speed (S) in units of ‘km/hr’. ” (a) What are the implied units for the “5.7” factor? Hint: recall that relations between physical quantities must be dimensionally consistent, and the chosen units must in turn be consistent with the dimensionality. (b) Re-write the equation so that it gives the maximum speed in units of “m/s” for a given body mass in “g”. Show all relevant details. If done correctly, you will need to use at least one unit conversion factor
The maximum running speed (S) in km/hr and the corresponding body mass (m) in kg were determined for 55 different species of mammals. An empirical relation was determined to be: S[km/hr] = 5.7 (m[kg])2 . Note: The notation in this equation means, “inserting the mass (m) in units of ‘kg’, automatically calculates the maximum running speed (S) in units of ‘km/hr’. ” (a) What are the implied units for the “5.7” factor? Hint: recall that relations between physical quantities must be dimensionally consistent, and the chosen units must in turn be consistent with the dimensionality. (b) Re-write the equation so that it gives the maximum speed in units of “m/s” for a given body mass in “g”. Show all relevant details. If done correctly, you will need to use at least one unit conversion factor
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The maximum running speed (S) in km/hr and the corresponding body mass (m) in kg were determined for 55 different species of mammals. An empirical relation was determined to be:
S[km/hr] = 5.7 (m[kg])2 . Note: The notation in this equation means, “inserting the mass (m) in units of ‘kg’, automatically calculates the maximum running speed (S) in units of ‘km/hr’. ”
(a) What are the implied units for the “5.7” factor? Hint: recall that relations between physical quantities must be dimensionally consistent, and the chosen units must in turn be consistent with the dimensionality.
(b) Re-write the equation so that it gives the maximum speed in units of “m/s” for a given body mass in “g”. Show all relevant details. If done correctly, you will need to use at least one unit conversion factor.
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