Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 6.5, Problem 18FP
Determine the moment of inertia of the cross-sectional area of the beam about the centroidal x and y axes.
Prob. F6-18
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Question 2 (40 Points)
Consider the following double pendulum-like system with links ₁ and 12. The angles 0 and & could have
angular velocities ėêk and êk, respectively, where ②k is a unit vector that points out of the page and is
perpendicular to x and y. They could also have angular accelerations Ök and êk. The angle is
defined relative to the angle 0. The link 12 is a spring and can extend or compress at a rate of 12. It can
also have a rate of extension or compression Ï2.
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y
êr1
êe
12
χ
3
еф
er2
ده لج
1) Express the velocity of the mass in terms of the unit vectors ê0, êr1, êø, and êr2, and any
extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points)
2) Express the acceleration of the mass in terms of the unit vectors ê¤, ê×1, êp, and êÃ2, and any
extension/contraction of the links (e.g.,. İ; and Ï¿) (12 Points)
3) Express the velocity of the mass in terms of unit vectors î and ĵ that point in the x and y
directions, respectively. Also include the appropriate,…
Chapter 6 Solutions
Statics and Mechanics of Materials (5th Edition)
Ch. 6.1 - In each case, use the element shown and specify...Ch. 6.1 - Prob. 1FPCh. 6.1 - Determine the centroid (x,y) of the area. Prob....Ch. 6.1 - Determine the centroid y of the area. Prob. F63Ch. 6.1 - Locate the center of gravity x of the straight rod...Ch. 6.1 - Prob. 5FPCh. 6.1 - Locate the centroid z of the homogeneous solid...Ch. 6.1 - Locate the centroid x of the area. Prob. 61Ch. 6.1 - Locate the centroid of the area. Prob. 62Ch. 6.1 - Locate the centroid x of the area. Probs. 63/4
Ch. 6.1 - Locate the centroid y of the area. Probs. 63/4Ch. 6.1 - Locate the centroid x of the area. Probs. 65/6Ch. 6.1 - Locate the centroid y of the area. Probs. 65/6Ch. 6.1 - Prob. 7PCh. 6.1 - Prob. 8PCh. 6.1 - Locate the centroid x of the area. Solve the...Ch. 6.1 - Prob. 10PCh. 6.1 - Prob. 11PCh. 6.1 - Prob. 12PCh. 6.1 - Locate the centroid y of the area. Probs. 612/13Ch. 6.1 - Prob. 14PCh. 6.1 - Prob. 15PCh. 6.1 - Prob. 16PCh. 6.1 - Locate the centroid x of the area. Probs. 617/18Ch. 6.1 - Prob. 18PCh. 6.1 - Prob. 19PCh. 6.1 - Locate the centroid x of the area. Probs. 620/21Ch. 6.1 - Locate the centroid y of the area. Probs. 620/21Ch. 6.1 - Locate the centroid x of the area. Probs. 622/23Ch. 6.1 - Prob. 23PCh. 6.1 - Prob. 24PCh. 6.1 - Prob. 25PCh. 6.1 - Prob. 26PCh. 6.1 - Prob. 27PCh. 6.1 - The steel plate is 0.3 m thick and has a density...Ch. 6.1 - Prob. 29PCh. 6.1 - Prob. 30PCh. 6.1 - Prob. 31PCh. 6.1 - Prob. 32PCh. 6.1 - Prob. 33PCh. 6.1 - Locate the centroid z of the volume. Prob. 634Ch. 6.1 - Prob. 35PCh. 6.2 - Locate the centroid (x,y,z) of the wire bent in...Ch. 6.2 - Locate the centroid y of the beams cross-sectional...Ch. 6.2 - Locate the centroid y of the beams cross-sectional...Ch. 6.2 - Prob. 10FPCh. 6.2 - Prob. 11FPCh. 6.2 - Prob. 12FPCh. 6.2 - Locate the centroid (x,y) of the area. Prob. 636Ch. 6.2 - Locate the centroid y for the beams...Ch. 6.2 - Locate the centroid y of the beam having the...Ch. 6.2 - Locate the centroid (x,y) of the area. Prob. 639Ch. 6.2 - Locate the centroid y of the beams cross-sectional...Ch. 6.2 - Locate the centroid (x,y) of the area. Prob. 641Ch. 6.2 - Locate the centroid (x,y) of the area. Prob. 642Ch. 6.2 - Prob. 43PCh. 6.2 - Locate the centroid y of the cross-sectional area...Ch. 6.2 - Prob. 45PCh. 6.2 - Prob. 46PCh. 6.2 - Prob. 47PCh. 6.2 - Prob. 48PCh. 6.2 - Prob. 49PCh. 6.2 - Prob. 50PCh. 6.2 - Prob. 51PCh. 6.2 - Locate the center of gravity z of the assembly....Ch. 6.2 - Major floor loadings in a shop are caused by the...Ch. 6.2 - The assembly consists of a 20-in. wooden dowel rod...Ch. 6.2 - The composite plate is made from both steel (A)...Ch. 6.4 - Determine the moment of inertia of the area about...Ch. 6.4 - Prob. 14FPCh. 6.4 - Prob. 15FPCh. 6.4 - Determine the moment of inertia of the area about...Ch. 6.4 - Prob. 56PCh. 6.4 - Prob. 57PCh. 6.4 - Prob. 58PCh. 6.4 - Prob. 59PCh. 6.4 - Determine the moment of inertia for the area about...Ch. 6.4 - Determine the moment of inertia for the area about...Ch. 6.4 - Prob. 62PCh. 6.4 - Prob. 63PCh. 6.4 - Prob. 64PCh. 6.4 - Prob. 65PCh. 6.4 - Prob. 66PCh. 6.4 - Prob. 67PCh. 6.4 - Prob. 68PCh. 6.4 - Prob. 69PCh. 6.4 - Prob. 70PCh. 6.4 - Prob. 71PCh. 6.4 - Prob. 72PCh. 6.4 - Prob. 73PCh. 6.4 - Prob. 74PCh. 6.4 - Prob. 75PCh. 6.4 - Prob. 76PCh. 6.4 - Determine the moment of inertia for the area about...Ch. 6.4 - Determine the moment of inertia for the area about...Ch. 6.4 - Prob. 79PCh. 6.5 - Determine the moment of inertia of the...Ch. 6.5 - Determine the moment of inertia of the...Ch. 6.5 - Prob. 19FPCh. 6.5 - Determine the moment of inertia of the...Ch. 6.5 - Determine the moment of inertia of the composite...Ch. 6.5 - Determine the moment of inertia of the composite...Ch. 6.5 - Prob. 82PCh. 6.5 - Determine the location y of the centroid of the...Ch. 6.5 - Determine y, which locates the centroidal axis x...Ch. 6.5 - Prob. 85PCh. 6.5 - Prob. 86PCh. 6.5 - Determine the moment of inertia Ix of the area...Ch. 6.5 - Determine the moment of inertia Ix of the area...Ch. 6.5 - Determine the moment of inertia of the...Ch. 6.5 - Determine y, which locates the centroidal axis x...Ch. 6.5 - Determine the moment of inertia of the...Ch. 6.5 - Determine the moment of inertia of the...Ch. 6 - Locate the centroid x of the area.Ch. 6 - Locate the centroid y of the area.Ch. 6 - Locate the centroid of the rod.Ch. 6 - Prob. 4RPCh. 6 - Determine the moment of inertia for the area about...Ch. 6 - Prob. 6RPCh. 6 - Determine the area moment of inertia of the...
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