SCIENCE+ENGR.OF MTRLS.,ENHANCED
7th Edition
ISBN: 9780357447864
Author: ASKELAND
Publisher: CENGAGE L
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Chapter 1, Problem 1.31P
To determine
To design: a composite material having density of
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Problem 1 (30 Points)
Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In
scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no
friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in
both scenarios, there is one generalized coordinate, .
R
Scenario 1
R
m
R
g
Scenario 2
m
HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the
bowl (scenario 1), or the pivot point of the pendulum (scenario 2).
Part I
a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points)
b) What can you say about the systems based on the Lagrangian? (2 points)
c) Solve for the equations of motion for both systems. (8 points)
Part II
Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to
determine the normal force acting on the mass.
a)…
Chapter 1 Solutions
SCIENCE+ENGR.OF MTRLS.,ENHANCED
Ch. 1 - Define materials science and engineering (MSE).Ch. 1 - What is the importance of the engineering...Ch. 1 - Define the following terms: Composition;...Ch. 1 - Explain the difference between the terms materials...Ch. 1 - The myriad materials in the world primarily fall...Ch. 1 - What are some of the materials and mechanical...Ch. 1 - What is a ceramic, and what are some of the...Ch. 1 - comparisons between thermoplastics and...Ch. 1 - Give three examples of composites that can be...Ch. 1 - For each of the followign classes of materials,...
Ch. 1 - Describe the enabling materials property of each...Ch. 1 - Describe the enabling materials property of each...Ch. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - Temperature indicators are sometimes produced from...Ch. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Prob. 1.20PCh. 1 - Steel is often coated with a thin layer of zinc if...Ch. 1 - Prob. 1.22PCh. 1 - Prob. 1.23PCh. 1 - Prob. 1.24PCh. 1 - You are an engineer working for a manufacturer of...Ch. 1 - We would like to produce a transparent canopy for...Ch. 1 - Prob. 1.27PCh. 1 - Prob. 1.28PCh. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Prob. 1.31PCh. 1 - You would like to be able to identify different...Ch. 1 - You would like to be able to physically separate...Ch. 1 - Some pistons for automobile engines might be...Ch. 1 - • Convert 7750kg/m3tolb/ft3 using the Unit...Ch. 1 - • Using the basic search option in Knovel, find as...Ch. 1 - Prob. 1.3KP
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