Vector Mechanics for Engineers: Statics
12th Edition
ISBN: 9781260501735
Author: BEER
Publisher: MCG
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Chapter 5.1, Problem 5.23P
PROBLEM 5.23
The first moment of the shaded area with respect to the x-axis is denoted by Qx. (a) Express Qx in terms of b, c, and the distance y from the base of the shaded area to the x-axis. (b) For what value of y is Qx maximum, and what is the maximum value?
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n this question, you will calculate the second moment of area for a 4 ✕ 6 piece of lumber about the x − x and y − y axes, as shown. A rectangle with height h and width w > h is centered on the origin of the x y-coordinate plane. The left and right sides of the rectangle, having height h, are parallel to the vertical y – y axis and the top and bottom sides, having width w, are parallel to the horizontal x – x axis. Visit a hardware store and measure the actual dimensions of a typical 4 ✕ 6 piece of lumber. (Enter your answers in inches.)
h = in
w = in
Calculate the second moment of area about the x − x and y − y axes using the measured dimensions. (Enter your answers in in.4.)
Ix – x = ______in4
Iy – y = ________in4
ABCD is rectangle in which AB=CD=100mm and BC=DA=80mm. Forces of 100N each act along AB and CD and forces of 50N each at along BC and DA. Find the resultant moment of the two couples.
A. -10,000 N-mm C. -20,000 N-mm
B. -13,000 N-mm D. -23,000 N-mm
Chapter 5 Solutions
Vector Mechanics for Engineers: Statics
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 - 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 - 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 - 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 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.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 - For the area shown, determine the ratio a/b for...Ch. 5.1 - For the semiannular area of Prob. 5.12, determine...Ch. 5.1 - A built-up beam is constructed by nailing seven...Ch. 5.1 - The horizontal x axis is drawn through the...Ch. 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 - A thin, homogeneous wire is bent to form the...Ch. 5.1 - A thin, homogeneous wire is bent to form the...Ch. 5.1 - A thin, homogeneous wire is bent to form the...Ch. 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 - Determine by direct integration the centroid of...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 - 5.48 and 5.49 Determine by direct integration the...Ch. 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 - Determine the volume and the surface area of the...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Determine the volume of the solid generated by...Ch. 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 - Determine the volume of the brass collar obtained...Ch. 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 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through Determine the reactions at the beam...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through Determine the reactions at the beam...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 - Determine the reactions at the beam supports for...Ch. 5.3 - Determine (a) the distributed load w0 at the end D...Ch. 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 - Prob. 5.84PCh. 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 - A cone and a cylinder of the same radius a and...Ch. 5.4 - Determine the location of the center of gravity of...Ch. 5.4 - Prob. 5.99PCh. 5.4 - For the stop bracket shown, locate the x...Ch. 5.4 - Fig. P5.100 and P5.101 5.101 For the stop bracket...Ch. 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 - Locate the center of gravity of the sheet-metal...Ch. 5.4 - Locate the center of gravity of the sheet-metal...Ch. 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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