Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing the units of the relevant quantities. Under the assumption that the pendulum's period can only depend on the pendulum's length L, mass m, maximum angle 0, and the strength of gravity g (with units [g]=m/s2), explain why we must have a relation like T = f(0) × √√.2 (Note that counts as a unitless parameter here.) Asserting ƒ(0) ~ f(0) in this formula is the small X 9 angle approximation (where f(0) = 2π is found by other means).
Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing the units of the relevant quantities. Under the assumption that the pendulum's period can only depend on the pendulum's length L, mass m, maximum angle 0, and the strength of gravity g (with units [g]=m/s2), explain why we must have a relation like T = f(0) × √√.2 (Note that counts as a unitless parameter here.) Asserting ƒ(0) ~ f(0) in this formula is the small X 9 angle approximation (where f(0) = 2π is found by other means).
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 89CP: The purpose of this problem is to show the entire concept of dimensional consistency can be...
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![Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing the units of the
relevant quantities. Under the assumption that the pendulum's period can only depend on the pendulum's length L, mass
m, maximum angle 0, and the strength of gravity g (with units [g]=m/s²), explain why we must have a relation like
T = f(0) × √2 (Note that counts as a unitless parameter here.) Asserting f(0) ~ ƒ(0) in this formula is the small
angle approximation (where f(0) = 2π is found by other means).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb489c6f-485f-4a8c-af24-f0100b31b711%2Fec5bea2f-47f4-4d6a-b831-708fbf0d2d94%2Fbhcodpo_processed.png&w=3840&q=75)
Transcribed Image Text:Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing the units of the
relevant quantities. Under the assumption that the pendulum's period can only depend on the pendulum's length L, mass
m, maximum angle 0, and the strength of gravity g (with units [g]=m/s²), explain why we must have a relation like
T = f(0) × √2 (Note that counts as a unitless parameter here.) Asserting f(0) ~ ƒ(0) in this formula is the small
angle approximation (where f(0) = 2π is found by other means).
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