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Determine whether each approximation is an overestimate or underestimate and give a qualitative reason why. For each approximation, compute the percentage difference from the exact value. How would the percentage difference change if the bar was more massive or longer?

Determine whether each approximation is an overestimate or underestimate and give a qualitative reason why. For each approximation, compute the percentage difference from the exact value. How would the percentage difference change if the bar was more massive or longer?

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)...
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Need help with pre lab questions! This is updated since last one was under wrong subject.
Overview: Here you will make successive approximations of the moment of inertia of a constant-density 1D bar when the pivot point is at one extreme end of the bar. You will model the bar first as a single point mass, followed by two-, three- and four-point mass approximations. In each case, you will compare the approximation with the exact value. The exact moment of inertia of a constant-density 1D rod of length L and mass M with pivot point at one extreme end is calculated in Example 12.5 on page 302 and has a value of lexact = The moment of inertia is then: 1 Procedure: For simplicity, let's model a bar of mass M=1kg and length L = Imeter. To approximate the continuous bar with N point masses, each point mass has a mass of mi = M/N. We then place the masses symmetrically with respect to the actual bar at positions xi. Iapprox ML² N • Σmax7. i=1 The positions x; can be worked out by inspecting the diagrams on the following page.
Transcribed Image Text:Overview: Here you will make successive approximations of the moment of inertia of a constant-density 1D bar when the pivot point is at one extreme end of the bar. You will model the bar first as a single point mass, followed by two-, three- and four-point mass approximations. In each case, you will compare the approximation with the exact value. The exact moment of inertia of a constant-density 1D rod of length L and mass M with pivot point at one extreme end is calculated in Example 12.5 on page 302 and has a value of lexact = The moment of inertia is then: 1 Procedure: For simplicity, let's model a bar of mass M=1kg and length L = Imeter. To approximate the continuous bar with N point masses, each point mass has a mass of mi = M/N. We then place the masses symmetrically with respect to the actual bar at positions xi. Iapprox ML² N • Σmax7. i=1 The positions x; can be worked out by inspecting the diagrams on the following page.
Continuous Bar 0 1 point-mass approximation 0 2 point-mass approximation 0 3 point-mass approximation 0 0 m=M/2 m₁=M/3 XI 4 point-mass approximation m₁=M/4 x₁ X1 m₂ M/4 X2 m₁=M X1 m₂=M/3 79000 X2 m₂=M/4 X3 m₂-M/2 X2 m3 M/3 X3 m4 M/4 L For each approximation, compute the percentage difference from the exact value. How would the percentage difference change if the bar was more massive or longer? Extra gradit (um 10 L L L Determine whether each approximation is an overestimate or underestimate and give a qualitative reason why. L x X x
Transcribed Image Text:Continuous Bar 0 1 point-mass approximation 0 2 point-mass approximation 0 3 point-mass approximation 0 0 m=M/2 m₁=M/3 XI 4 point-mass approximation m₁=M/4 x₁ X1 m₂ M/4 X2 m₁=M X1 m₂=M/3 79000 X2 m₂=M/4 X3 m₂-M/2 X2 m3 M/3 X3 m4 M/4 L For each approximation, compute the percentage difference from the exact value. How would the percentage difference change if the bar was more massive or longer? Extra gradit (um 10 L L L Determine whether each approximation is an overestimate or underestimate and give a qualitative reason why. L x X x
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