Vector Mechanics for Engineers: Statics
12th Edition
ISBN: 9781259977268
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5.2, Problem 5.45P
5.45 and 5.46
A homogeneous wire is bent into the shape shown. Determine by direct integration the x coordinate of its centroid.
Fig. P5.45
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem4.
The thin uniform disk of mass m = 1-kg and radius R = 0.1m spins about the bent shaft OG with
the angular speed w2 = 20 rad/s. At the same time, the shaft rotates about the z-axis with the angular
speed 001 = 10 rad/s. The angle between the bent portion of the shaft and the z-axis is ẞ = 35°. The
mass of the shaft is negligible compared to the mass of the disk.
a. Find the angular momentum of the disk with respect to point G, based on the axis
orientation as shown. Include an MVD in your solution.
b. Find the angular momentum of the disk with respect to point O, based on the axis
orientation as shown. (Note: O is NOT the center of fixed-point rotation.)
c. Find the kinetic energy of the assembly.
z
R
R
002
2R
x
Answer: H = -0.046ĵ-0.040 kg-m²/sec
Ho=-0.146-0.015 kg-m²/sec
T 0.518 N-m
=
Problem 3.
The assembly shown consists of a solid sphere of mass m and the uniform slender rod of the same
mass, both of which are welded to the shaft. The assembly is rotating with angular velocity w at a
particular moment. Find the angular momentum with respect to point O, in terms of the axes
shown.
Answer: Ñ。 = ½mc²wcosßsinßĵ + (}{mr²w + 2mb²w + ½ mc²wcos²ß) k
3
m
r
b
2
C
لا
m
Only question 2
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...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Only question 1arrow_forwardOnly question 3arrow_forwardI have Euler parameters that describe the orientation of N relative to Q, e = -0.7071*n3, e4 = 0.7071. I have Euler parameters that describe the orientation of U relative to N, e = -1/sqrt(3)*n1, e4 = sqrt(2/3). After using euler parameter rule of successive rotations, I get euler parameters that describe the orientation of U relative to Q, e = -0.4082*n1 - 0.4082*n2 - 0.5774*n3. I need euler parameters that describe the orientation of U relative to Q in vector basis of q instead of n. How do I get that?arrow_forward
- Describe at least 4 processes in engineering where control charts are (or should be) appliedarrow_forwardDescribe at least two (2) processes where control charts are (or should be) applied.arrow_forwardProblem 3: A cube-shaped spacecraft is in a circular Earth orbit. Let N (n,) be inertial and the spacecraft is denoted S (ŝ₁). The spacecraft is described such that ¯½º = J ŝ₁ŝ₁ + J ŝ₂§₂ + J §¸Ŝ3 Location of the spacecraft in the orbit is determined by the orbit-fixed unit vectors ê, that are oriented by the angle (Qt), where is a constant angular rate. 52 €3 3> 2t 55 Λ Из At the instant when Qt = 90°, the spacecraft S is oriented relative to the orbit such that 8₁ = 0° Space-three 1-2-3 angles 0₂ = 60° and ES = $₂ rad/s 0₁ = 135° (a) At this instant, determine the direction cosine matrix that describes the orientation of the spacecraft with respect to the inertial frame N.arrow_forward
- This problem illustrates that the factor of safety for a machine element depends on the particular point selected for analysis. Here you are to compute factors of safety, based upon the distortion-energy theory, for stress elements at A and B of the member shown in the figure. This bar is made of AISI 1006 cold-drawn steel and is loaded by the forces F = 1.100 kN, P = 8.00 kN, and T = 50.00 N-m. Given: Sy = 280 MPa. B -100 mm- 15-mm D. a) Determine the value of the axial stress at point B. b) Determine the value of the shear stress at point B. c) Determine the value of the Von Mises stress at point B. P Farrow_forwardA piston-cylinder device initially contains 0.08 m^3 of nitrogen gas at 130 kPa and 170°C. The nitrogen is expanded to a pressure of 80 kPa via isentropic expansion. Determine the final temperature and the boundary work done by the system during this process.arrow_forwardA Carnot (ideal) heat pump is to be used to heat a house and maintain it at 22°C in winter. On a day when the average outdoor temperature remains at about 0°C, the house is estimated to lose heat at a rate of 65,000 kJ/h. If the heat pump consumes 6 kW of power while operating, determine: (a) how long the heat pump ran on that day (b) the total heating costs, assuming an average price of 11¢/kWh for electricity (c) the heating cost for the same day if an 85% efficient electric furnace is used instead of a heat pump.arrow_forward
- From the information in the image, I needed to find the orientation of U relative to Q in vector basis q_hat. I transformed the euler angle/axis representation to euler parameters. Then I got its conjugate in order to get the euler parameter in N frame relative to Q. The problem gave the euler angle/axis representation in Q frame relative to N, so I needed to find the conjugate. Then I used the euler parameter rule of successive rotation to find the final euler parameters that describe the orientation of U relative to Q. However that orientation is in n_hat which is the intermediate frame. How do I get the final result in q_hat?arrow_forwardA proposed method of power generation involves collecting and storing solar energy in large artificial lakes a few meters deep, called solar ponds. Solar energy is absorbed by all parts of the pond, and the water temperature rises everywhere. The top part of the pond, however, loses much of the heat it absorbs to the atmosphere, and as a result, the cool surface water serves as insulation for the bottom part of the pond and helps trap the energy there. Usually, salt is planted at the bottom of the pond to prevent the rise of this hot water to the top. A heat engine that uses an organic fluid, such as alcohol, as the working fluid can be operated between the top and the bottom portions of the pond. If the water temperature is 27°C near the surface and 72°C near the bottom of the pond, determine the maximum thermal efficiency that this power plant can have. Treat the cycle as an ideal heat engine. Would a heat engine operating under these temperature conditions (27°C and 72°C) be…arrow_forwardA standard Carnot heat engine cycle is executed in a closed system between the temperature limits of 320 and 1350 K, with air as the working fluid. The pressures before and after the isothermal compression are 150 and 300 kPa, respectively. Sketch the TS diagram for this cycle. If the net work output per cycle is 0.75 kJ, determine the efficiency of the cycle and the heat transfer to the air (working fluid) per cycle.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
Mechanical Engineering: Centroids & Center of Gravity (1 of 35) What is Center of Gravity?; Author: Michel van Biezen;https://www.youtube.com/watch?v=Tkyk-G1rDQg;License: Standard Youtube License