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Automotive Technology
7th Edition
ISBN: 9781337794213
Author: ERJAVEC, Jack.
Publisher: Cengage,
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Chapter 45, Problem 3SA
To determine
The reason for the recommendation of tire rotation by most manufacturers.
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The heated rod from Problem 3 is subject to a volumetric heating
h(x) = h0
x
L in units of [Wm−3], as shown in the figure below. Under the
heat supply the temperature of the rod changes along x with the
temperature function T (x). The temperature T (x) is governed by the
d
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dx (q(x)) + h(x) = 0 PDE
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where q(x) is the heat flux through the rod and k is the (constant)
thermal conductivity. Both ends of the bar are in contact with a heat
reservoir at zero temperature.
Determine:
1. Appropriate BCs for this physical problem.
2. The temperature function T (x).
3. The heat flux function q(x).
Side Note: Please see that both ends of bar are in contact with a heat reservoir at zero temperature so the boundary condition at the right cannot be du/dx=0 because its not thermally insulated. Thank you
The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω2x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement d u(x) is governed by the following equations: dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L. Determine: 1. Appropriate BCs for this physical problem. 2. The displacement function u(x). 3. The stress function σ(x). SIDE QUESTION: I saw a tutor solve it before but I didn't understand why the tutor did not divide E under the second term (c1x) before finding u(x). The tutor only divided E under first term. please explain and thank you
Chapter 45 Solutions
Automotive Technology
Ch. 45 - List five things that could cause premature...Ch. 45 - Define lateral and radial runout.Ch. 45 - Prob. 3SACh. 45 - Define dynamic and static wheel balance.Ch. 45 - Describe the proper procedure to seal a puncture...Ch. 45 - The rim offset is the vertical distance between...Ch. 45 - Prob. 7SACh. 45 - Explain why a TPMS relearn should be performed...Ch. 45 - A tire that wobbles from side-to-side is said to...Ch. 45 - A front tire has excessive wear on both edges of...
Ch. 45 - All of the following statements are correct...Ch. 45 - All of the following statements are correct...Ch. 45 - Which of the following statements about sidewall...Ch. 45 - All of these statements about improper wheel...Ch. 45 - Prob. 7MCCh. 45 - Technician A says that the front wheel bearings on...Ch. 45 - Technician A says that dynamic wheel imbalance...Ch. 45 - Technician A says that front bearing assembly...Ch. 45 - Technician A says that replacement wheel rims...Ch. 45 - Prob. 5ASRQCh. 45 - While choosing the correct tire for a vehicle:...Ch. 45 - Technician A says that on most vehicles, the...Ch. 45 - Prob. 8ASRQCh. 45 - Prob. 9ASRQCh. 45 - Prob. 10ASRQ
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