Vector Mechanics for Engineers: Statics, 11th Edition
Vector Mechanics for Engineers: Statics, 11th Edition
11th Edition
ISBN: 9780077687304
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek
Publisher: McGraw-Hill Education
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Chapter 5.4, Problem 5.130P

Show that for a regular pyramid of height h and n sides (n = 3, 4,...) the centroid of the volume of the pyramid is located at a distance h/4 above the base.

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Show that for a regular pyramid of height h and n sides (n = 3, 4, . . .) the centroid of the volume of the pyramid is located at a distance h /4 above the base.
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Chapter 5 Solutions

Vector Mechanics for Engineers: Statics, 11th Edition

Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.
Ch. 5.1 - 5.10 through 5.15 Locate the centroid of the plane...Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - 5.10 through 5.15 Locate the centroid of the plane...Ch. 5.1 - 5.10 through 5.15 Locate the centroid of the plane...Ch. 5.1 - 5.10 through 5.15 Locate the centroid of the plane...Ch. 5.1 - PROBLEM 5.16 Determine the y coordinate of the...Ch. 5.1 - Show that as r1 approaches r2, the location of the...Ch. 5.1 - Prob. 5.18PCh. 5.1 - For the semiannular area of Prob. 5.12, determine...Ch. 5.1 - Prob. 5.20PCh. 5.1 - Prob. 5.21PCh. 5.1 - The horizontal x-axis is drawn through the...Ch. 5.1 - PROBLEM 5.23 The first moment of the shaded area...Ch. 5.1 - Prob. 5.24PCh. 5.1 - Prob. 5.25PCh. 5.1 - Prob. 5.26PCh. 5.1 - A thin, homogeneous wire is bent to form the...Ch. 5.1 - The homogeneous wire ABC is bent into a...Ch. 5.1 - The frame for a sign is fabricated from thin, flat...Ch. 5.1 - The homogeneous wire ABCD is bent as shown and is...Ch. 5.1 - The homogeneous wire ABCD is bent as shown and is...Ch. 5.1 - Determine the distance h for which the centroid of...Ch. 5.1 - Knowing that the distance h has been selected to...Ch. 5.2 - 5.34 through 5.36 Determine by direct integration...Ch. 5.2 - 5.34 through 5.36 Determine by direct integration...Ch. 5.2 - 5.34 through 5.36 Determine by direct integration...Ch. 5.2 - 5.37 through 5.39 Determine by direct integration...Ch. 5.2 - 5.37 through 5.39 Determine by direct integration...Ch. 5.2 - 5.37 through 5.39 Determine by direct integration...Ch. 5.2 - 5.40 and 5.41 Determine by direct integration the...Ch. 5.2 - 5.40 and 5.41 Determine by direct integration the...Ch. 5.2 - Determine by direct integration the centroid of...Ch. 5.2 - 5.43 and 5.44 Determine by direct integration the...Ch. 5.2 - 5.43 and 5.44 Determine by direct integration the...Ch. 5.2 - 5.45 and 5.46 A homogeneous wire is bent into the...Ch. 5.2 - 5.45 and 5.46 A homogeneous wire is bent into the...Ch. 5.2 - A homogeneous wire is bent into the shape shown....Ch. 5.2 - 5.48 and 5.49 Determine by direct integration the...Ch. 5.2 - Prob. 5.49PCh. 5.2 - Determine the centroid of the area shown in terms...Ch. 5.2 - Determine the centroid of the area shown when a =...Ch. 5.2 - Prob. 5.52PCh. 5.2 - 5.53 Determine the volume and the surface area of...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Prob. 5.55PCh. 5.2 - Prob. 5.56PCh. 5.2 - Verify that the expressions for the volumes of the...Ch. 5.2 - Knowing that two equal caps have been removed from...Ch. 5.2 - Three different drive belt profiles are to be...Ch. 5.2 - Determine the capacity, in liters, of the punch...Ch. 5.2 - Determine the volume and total surface area of the...Ch. 5.2 - Determine the volume and weight of the solid brass...Ch. 5.2 - Determine the total surface area of the solid...Ch. 5.2 - Prob. 5.64PCh. 5.2 - The shade for a wall-mounted light is formed from...Ch. 5.3 - 5.66 and 5.67 For the beam and loading shown,...Ch. 5.3 - 5.66 and 5.67 For the beam and loading shown,...Ch. 5.3 - Prob. 5.68PCh. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - Determine (a) the distance a so that the vertical...Ch. 5.3 - Determine (a) the distance a so that the reaction...Ch. 5.3 - Prob. 5.76PCh. 5.3 - Prob. 5.77PCh. 5.3 - The beam AB supports two concentrated loads and...Ch. 5.3 - For the beam and loading of Prob. 5.78, determine...Ch. 5.3 - The cross section of a concrete dam is as shown....Ch. 5.3 - The cross section of a concrete dam is as shown....Ch. 5.3 - The dam for a lake is designed to withstand the...Ch. 5.3 - The base of a dam for a lake is designed to resist...Ch. 5.3 - 5.84 An automatic valve consists of a 9 × 9-in....Ch. 5.3 - Prob. 5.85PCh. 5.3 - The 3 4-m side AB of a tank is hinged at its...Ch. 5.3 - The 3 4-m side of an open tank is hinged at its...Ch. 5.3 - A 0.5 0.8-m gate AB is located at the bottom of a...Ch. 5.3 - A 0.5 0.8-m gate AB is located at the bottom of a...Ch. 5.3 - A 4 2-ft gate is hinged at A and is held in...Ch. 5.3 - Fig. P5.90 5.91 Solve Prob. 5.90 if the gate...Ch. 5.3 - A prismatically shaped gate placed at the end of a...Ch. 5.3 - A prismatically shaped gate placed at the end of a...Ch. 5.3 - A long trough is supported by a continuous hinge...Ch. 5.3 - The square gate AB is held in the position shown...Ch. 5.4 - Consider the composite body shown. Determine (a)...Ch. 5.4 - Prob. 5.97PCh. 5.4 - Prob. 5.98PCh. 5.4 - Prob. 5.99PCh. 5.4 - Prob. 5.100PCh. 5.4 - Prob. 5.101PCh. 5.4 - Prob. 5.102PCh. 5.4 - Prob. 5.103PCh. 5.4 - For the machine element shown, locate the y...Ch. 5.4 - For the machine element shown, locate the x...Ch. 5.4 - 5.106 and 5.107 Locate the center of gravity of...Ch. 5.4 - 5.106 and 5.107 Locate the center of gravity of...Ch. 5.4 - A corner reflector for tracking by radar has two...Ch. 5.4 - A wastebasket, designed to fit in the corner of a...Ch. 5.4 - An elbow for the duct of a ventilating system is...Ch. 5.4 - A window awning is fabricated from sheet metal...Ch. 5.4 - Prob. 5.112PCh. 5.4 - Prob. 5.113PCh. 5.4 - A thin steel wire with a uniform cross section is...Ch. 5.4 - The frame of a greenhouse is constructed from...Ch. 5.4 - Locate the center of gravity of the figure shown,...Ch. 5.4 - Prob. 5.117PCh. 5.4 - A scratch awl has a plastic handle and a steel...Ch. 5.4 - PROBLEM 5.117 A bronze bushing is mounted inside a...Ch. 5.4 - PROBLEM 5.120 A brass collar, of length 2.5 in.,...Ch. 5.4 - PROBLEM 5.121 The three legs of a small...Ch. 5.4 - Prob. 5.122PCh. 5.4 - Determine by direct integration the values of x...Ch. 5.4 - Prob. 5.124PCh. 5.4 - PROBLEM 5.125 Locate the centroid of the volume...Ch. 5.4 - Prob. 5.126PCh. 5.4 - Prob. 5.127PCh. 5.4 - PROBLEM 5.128 Locate the centroid of the volume...Ch. 5.4 - PROBLEM 5.129 Locate the centroid of the volume...Ch. 5.4 - Show that for a regular pyramid of height h and n...Ch. 5.4 - PROBLEM 5.131 Determine by direct integration the...Ch. 5.4 - PROBLEM 5.132 The sides and the base of a punch...Ch. 5.4 - Locate the centroid of the section shown, which...Ch. 5.4 - Locate the centroid of the section shown, which...Ch. 5.4 - Determine by direct integration the location of...Ch. 5.4 - Alter grading a lot, a builder places four stakes...Ch. 5 - 5.137 and 5.138 Locate the centroid of the plane...Ch. 5 - 5.137 and 5.138 Locate the centroid of the plane...Ch. 5 - Prob. 5.139RPCh. 5 - Determine by direct integration the centroid of...Ch. 5 - Determine by direct integration the centroid of...Ch. 5 - The escutcheon (a decorative plate placed on a...Ch. 5 - Determine the reactions at the supports for the...Ch. 5 - A beam is subjected to a linearly distributed...Ch. 5 - A tank is divided into two sections by a 1 1-m...Ch. 5 - Determine the y coordinate of the centroid of the...Ch. 5 - An 8-in.-diameter cylindrical duct and a 4 8-in....Ch. 5 - Three brass plates are brazed to a steel pipe to...
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