Homework Help is Here – Start Your Trial Now!
Science
Physics
Consider a thin hoop of mass (1.420 ± 0.001) kg and radius  (0.250 ± 0.002) m. The moment of inertia for a thin hoop rotating about an axis going through its center is MR2 . Calculate the moment of inertia of this hoop and its uncertainty using error propagation rules (see Appendix). Clearly show work.  Please solve the uncertainty using the appendix I attached

Consider a thin hoop of mass (1.420 ± 0.001) kg and radius  (0.250 ± 0.002) m. The moment of inertia for a thin hoop rotating about an axis going through its center is MR2 . Calculate the moment of inertia of this hoop and its uncertainty using error propagation rules (see Appendix). Clearly show work.  Please solve the uncertainty using the appendix I attached

College Physics
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)...
See similar textbooks
icon
Related questions
Question

Consider a thin hoop of mass (1.420 ± 0.001) kg and radius  (0.250 ± 0.002) m. The moment of inertia for a thin hoop rotating about an axis going through its center is MR2 . Calculate the moment of inertia of this hoop and its uncertainty using error propagation rules (see Appendix). Clearly show work. 

Please solve the uncertainty using the appendix I attached 

 

Experimental Errors and Uncertainties Propagation of Uncertainties Often, the quantity of interest cannot be determined in a one-step measurement (for example, area of a rectangle using a ruler). We combine several measurements, each with their associated uncertainties, into an equation. These uncertainties propagate (are carried) into the uncertainty of the final answer. Rules for propagation of uncertainties Let z be a quantity determined from combination of two direct measurements, x ± Ax and y+Ay. The uncertainty of z, Az, depends on how the three quantities mathematically relate to each other. of In general, for any function of two variables, z = f(x, y), the uncertainly is Az = (24) ² (Ax)² + (Ay)². V Some of the most common cases, all derived from the general formula above, are shown in the table below. Addition/Subtraction Multiplication Division Power Multiplication by a constant Logarithms Examples of propagation of uncertainties 1. Addition z = x+y z = xy Z = y z = x² z = ax z = ln(x) z = log(x) AL = V /0.052 +0.052 = 0.07cm L = 28.50 +0.07cm Note that the quantity and its uncertainty should be reported using the same units. Az = √√(Ax)² + (Ay)² 2 Az = |xyl (+)² + (²²) ² 2 - H²)²+(² 0.2 Az = Az = |n|x-¹Ax Az = |a|Ax Ax Az = - X 1 Ax In(10) x Az = You need to measure the length of a table of roughly 30 cm and you have a 20 cm ruler available. Naturally, you need to take two measurements. Your measurements are 20.00 cm and 8.50 cm, each of them having an uncertainly of ±0.05cm (only considering the instrumental uncertainty of the ruler). Determine the length of the table, L and its uncertainty, AL. L = 20.00cm + 8.50cm = 28.50cm 2 2. Division An object travels a certain distance, d, with constant speed and you want to determine this speed, and its associated uncertainty, from time and distance measurements. You measure the time to be t = 5.3 ± 0.2s and the distance d = 2.355 ± 0.001m. d v=== 2.3550m 5.3s ≈ 0.444 m/s 2 (0.001 Av= √(²)² + (²²) ² = 0.44 m/s ≈ 0.016 m/s V 2.355. Considering the rules for rounding numbers, the final answer will be: v= 0.44 ± 0.02 m/s
Transcribed Image Text:Experimental Errors and Uncertainties Propagation of Uncertainties Often, the quantity of interest cannot be determined in a one-step measurement (for example, area of a rectangle using a ruler). We combine several measurements, each with their associated uncertainties, into an equation. These uncertainties propagate (are carried) into the uncertainty of the final answer. Rules for propagation of uncertainties Let z be a quantity determined from combination of two direct measurements, x ± Ax and y+Ay. The uncertainty of z, Az, depends on how the three quantities mathematically relate to each other. of In general, for any function of two variables, z = f(x, y), the uncertainly is Az = (24) ² (Ax)² + (Ay)². V Some of the most common cases, all derived from the general formula above, are shown in the table below. Addition/Subtraction Multiplication Division Power Multiplication by a constant Logarithms Examples of propagation of uncertainties 1. Addition z = x+y z = xy Z = y z = x² z = ax z = ln(x) z = log(x) AL = V /0.052 +0.052 = 0.07cm L = 28.50 +0.07cm Note that the quantity and its uncertainty should be reported using the same units. Az = √√(Ax)² + (Ay)² 2 Az = |xyl (+)² + (²²) ² 2 - H²)²+(² 0.2 Az = Az = |n|x-¹Ax Az = |a|Ax Ax Az = - X 1 Ax In(10) x Az = You need to measure the length of a table of roughly 30 cm and you have a 20 cm ruler available. Naturally, you need to take two measurements. Your measurements are 20.00 cm and 8.50 cm, each of them having an uncertainly of ±0.05cm (only considering the instrumental uncertainty of the ruler). Determine the length of the table, L and its uncertainty, AL. L = 20.00cm + 8.50cm = 28.50cm 2 2. Division An object travels a certain distance, d, with constant speed and you want to determine this speed, and its associated uncertainty, from time and distance measurements. You measure the time to be t = 5.3 ± 0.2s and the distance d = 2.355 ± 0.001m. d v=== 2.3550m 5.3s ≈ 0.444 m/s 2 (0.001 Av= √(²)² + (²²) ² = 0.44 m/s ≈ 0.016 m/s V 2.355. Considering the rules for rounding numbers, the final answer will be: v= 0.44 ± 0.02 m/s
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Gibbs free Energy
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.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS