EBK FUNDAMENTALS OF MATERIALS SCIENCE A
5th Edition
ISBN: 9781119175506
Author: RETHWISCH
Publisher: JOHN WILEY+SONS INC.
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Chapter 3.21, Problem 25QP
To determine
The validation of the fact that the minimum cation to anion radius is
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Problem 1.
Two uniform rods AB and CE, each of weight 3 lb and length 2 ft, are welded to each other at their
midpoints. Knowing that this assembly has an angular velocity of constant magnitude c = 12 rad/s,
determine:
(1). the magnitude and direction of the angular momentum HD of the assembly about D.
(2). the dynamic reactions (ignore mg) at the bearings at A and B.
9 in.
3 in.
03
9 in.
3 in.
Answers: HD = 0.162 i +0.184 j slug-ft²/s
HG = 2.21 k
Ay =-1.1 lb; Az = 0; By = 1.1 lb; B₂ = 0.
Problem 5 (Optional, extra 6 points)
A 6-lb homogeneous disk of radius 3 in. spins as shown at the constant rate w₁ = 60 rad/s. The disk
is supported by the fork-ended rod AB, which is welded to the vertical shaft CBD. The system is
at rest when a couple Mo= (0.25ft-lb)j is applied to the shaft for 2 s and then removed. Determine
the dynamic reactions at C and D before and after the couple has been removed at 2 s.
4 in.
C
B
Mo
5 in
4 in.
Note: 2 rotating around CD induced by Mo is NOT
constant before Mo is removed.
and ₂ (two
unknowns) are related by the equation: ₂ =0+ w₂t
3 in.
Partial Answer (after Mo has been removed):
C-7.81+7.43k lb
D -7.81 7.43 lb
Problem 4.
A homogeneous disk with radius and mass m is mounted on an axle OG with length L and a
negligible mass. The axle is pivoted at the fixed-point O, and the disk is constrained to roll on a
horizontal surface. The disk rotates counterclockwise at the constant rate o₁ about the axle. (mg
must be included into your calculation)
(a). Calculate the linear velocity of G and indicate it on the figure.
(b). Calculate ₂ (constant), which is the angular velocity of the
axle OG around the vertical axis.
(c). Calculate the linear acceleration ā of G and indicate it on the
figure.
(d). Determine the force (assumed vertical) exerted by the floor on
the disk
(e). Determine the reaction at the pivot O.
1
Answers: N = mg +mr(r/L)² @² |j
mr w
IIG
C
R
L
i+
2L
=
Chapter 3 Solutions
EBK FUNDAMENTALS OF MATERIALS SCIENCE A
Ch. 3.21 - Prob. 1QPCh. 3.21 - Prob. 2QPCh. 3.21 - Prob. 3QPCh. 3.21 - Prob. 4QPCh. 3.21 - Prob. 5QPCh. 3.21 - Prob. 6QPCh. 3.21 - Prob. 7QPCh. 3.21 - Prob. 8QPCh. 3.21 - Prob. 9QPCh. 3.21 - Prob. 10QP
Ch. 3.21 - Prob. 11QPCh. 3.21 - Prob. 12QPCh. 3.21 - Prob. 13QPCh. 3.21 - Prob. 14QPCh. 3.21 - Prob. 15QPCh. 3.21 - Prob. 16QPCh. 3.21 - Prob. 17QPCh. 3.21 - Prob. 18QPCh. 3.21 - Prob. 19QPCh. 3.21 - Prob. 20QPCh. 3.21 - Prob. 21QPCh. 3.21 - Prob. 22QPCh. 3.21 - Prob. 23QPCh. 3.21 - Prob. 24QPCh. 3.21 - Prob. 25QPCh. 3.21 - Prob. 26QPCh. 3.21 - Prob. 27QPCh. 3.21 - Prob. 28QPCh. 3.21 - Prob. 29QPCh. 3.21 - Prob. 30QPCh. 3.21 - Prob. 31QPCh. 3.21 - Prob. 32QPCh. 3.21 - Prob. 33QPCh. 3.21 - Prob. 34QPCh. 3.21 - Prob. 35QPCh. 3.21 - Prob. 36QPCh. 3.21 - Prob. 37QPCh. 3.21 - Prob. 38QPCh. 3.21 - Prob. 39QPCh. 3.21 - Prob. 40QPCh. 3.21 - Prob. 41QPCh. 3.21 - Prob. 42QPCh. 3.21 - Prob. 43QPCh. 3.21 - Prob. 44QPCh. 3.21 - Prob. 45QPCh. 3.21 - Prob. 46QPCh. 3.21 - Prob. 47QPCh. 3.21 - Prob. 48QPCh. 3.21 - Prob. 49QPCh. 3.21 - Prob. 50QPCh. 3.21 - Prob. 53QPCh. 3.21 - Prob. 54QPCh. 3.21 - Prob. 55QPCh. 3.21 - Prob. 56QPCh. 3.21 - Prob. 57QPCh. 3.21 - Prob. 58QPCh. 3.21 - Prob. 59QPCh. 3.21 - Prob. 60QPCh. 3.21 - Prob. 61QPCh. 3.21 - Prob. 62QPCh. 3.21 - Prob. 63QPCh. 3.21 - Prob. 64QPCh. 3.21 - Prob. 65QPCh. 3.21 - Prob. 66QPCh. 3.21 - Prob. 67QPCh. 3.21 - Prob. 68QPCh. 3.21 - Prob. 69QPCh. 3.21 - Prob. 70QPCh. 3.21 - Prob. 71QPCh. 3.21 - Prob. 72QPCh. 3.21 - Prob. 73QPCh. 3.21 - Prob. 74QPCh. 3.21 - Prob. 75QPCh. 3.21 - Prob. 76QPCh. 3.21 - Prob. 77QPCh. 3.21 - Prob. 78QPCh. 3.21 - Prob. 79QPCh. 3.21 - Prob. 80QPCh. 3.21 - Prob. 81QPCh. 3.21 - Prob. 82QPCh. 3.21 - Prob. 83QPCh. 3.21 - Prob. 84QPCh. 3.21 - Prob. 85QPCh. 3.21 - Prob. 86QPCh. 3.21 - Prob. 87QPCh. 3.21 - Prob. 88QPCh. 3.21 - Prob. 89QPCh. 3.21 - Prob. 90QPCh. 3.21 - Prob. 91QPCh. 3.21 - Prob. 92QPCh. 3.21 - Prob. 93QPCh. 3.21 - Prob. 94QPCh. 3.21 - Prob. 95QPCh. 3.21 - Prob. 96QPCh. 3.21 - Prob. 97QPCh. 3.21 - Prob. 98QPCh. 3.21 - Prob. 99QPCh. 3.21 - Prob. 100QPCh. 3.21 - Prob. 101QPCh. 3.21 - Prob. 102QPCh. 3.21 - Prob. 103QPCh. 3.21 - Prob. 1SSPCh. 3.21 - Prob. 1FEQPCh. 3.21 - Prob. 2FEQPCh. 3.21 - Prob. 3FEQPCh. 3.21 - Prob. 4FEQPCh. 3.21 - Prob. 5FEQP
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- Problem 2. The homogeneous disk of weight W = 6 lb rotates at the constant rate co₁ = 16 rad/s with respect to arm ABC, which is welded to a shaft DCE rotating at the constant rate 2 = 8 rad/s. Assume the rod weight is negligible compared to the disk. Determine the dynamic reactions at D and E (ignore mg). Answers: D=-7.12ĵ+4.47k lb r-8 in. 9 in. B D E=-1.822+4.47 lb 9 in. E 12 in. 12 in. xarrow_forwardProblem 3. Each of the right angle rods has a mass of 120 g and is welded to the shaft, which rotates at a steady speed of 3600 rpm. Ignore the weight of the shaft AB. Find the bearing dynamic reaction at A due to the dynamic imbalance of the shaft. (ignore mgs) 100 N A 100 100 100 100 100 (Dimensions in millimeters) Answer: A=-8521-426j N Barrow_forwardHow to determine horizontal displacement of a framearrow_forward
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