Vector Mechanics for Engineers: Statics and Dynamics
12th Edition
ISBN: 9781259638091
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 19.1, Problem 19.27P
From
Fig. P19.27
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
From mechanics of materials it is known that when a static load P is applied at the end B of a uniform metal rod fixed at end A, the length of the rod will increase by an amount δ=PL/AE, where L is the length of the undeformed rod, A is its cross- sectional area, and E is the modulus of elasticity of the metal. Knowing that L = 450 mm and E = 200 GPa and that the diameter of the rod is 8 mm, and neglecting the mass of the rod, determine (a) the equivalent spring constant of the rod, (b ) the frequency of the vertical vibrations of a block of mass m = 8 kg attached to end B of the same rod.
A 350-kg machine is placed at the end of 1.8-m-long steel ( E = 210 x 109 N/m2)cantilever beam. The machine is observed to vibrate with a natural frequency of 35Hz.What is the moment of inertia of the beam's cross section about its neutral axis?
A conservative mechanical system consists of a mass m that is constrained to move along a circle of radius
R. The centre of the circle is at the origin O of the coordinate system. The mass is connected to a point A
along the â-axis at a distance 2R from the centre of circle with a spring of elastic constant k, so that the
corresponding elastic potential has the form Vspring = (k/2)ď², where d is the (varying) distance between the
mass and point A. Gravity acts, as usual, along the vertical direction. See the figure for a depiction of the
system.
0
m
(b) Write down the Lagrangian of the system.
(a) How many degrees of freedom does the system have? Indicate generalised coordinates to describe the
motion of the system.
X
(c) Write down the corresponding Euler-Lagrange equation(s).
Chapter 19 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3PCh. 19.1 - Prob. 19.4PCh. 19.1 - Prob. 19.5PCh. 19.1 - Prob. 19.6PCh. 19.1 - Prob. 19.7PCh. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9PCh. 19.1 - Prob. 19.10P
Ch. 19.1 - Prob. 19.11PCh. 19.1 - Prob. 19.12PCh. 19.1 - Prob. 19.13PCh. 19.1 - Prob. 19.14PCh. 19.1 - A 5-kg collar C is released from rest in the...Ch. 19.1 - Prob. 19.16PCh. 19.1 - Prob. 19.17PCh. 19.1 - An 11-lb block is attached to the lower end of a...Ch. 19.1 - Block A has a mass m and is supported by the...Ch. 19.1 - A 13.6-kg block is supported by the spring...Ch. 19.1 - Prob. 19.21PCh. 19.1 - 19.21 and 19.22A 50-kg block is supported by the...Ch. 19.1 - Prob. 19.23PCh. 19.1 - The period of vibration of the system shown is...Ch. 19.1 - Prob. 19.25PCh. 19.1 - Prob. 19.26PCh. 19.1 - From mechanics of materials, it is known that for...Ch. 19.1 - From mechanics of materials it is known that when...Ch. 19.1 - Prob. 19.29PCh. 19.1 - Prob. 19.30PCh. 19.1 - If h = 700 mm and d = 500 mm and each spring has a...Ch. 19.1 - Prob. 19.32PCh. 19.1 - Prob. 19.33PCh. 19.1 - Prob. 19.34PCh. 19.1 - Prob. 19.35PCh. 19.1 - Prob. 19.36PCh. 19.2 - The 9-kg uniform rod AB is attached to springs at...Ch. 19.2 - Prob. 19.38PCh. 19.2 - Prob. 19.39PCh. 19.2 - Prob. 19.40PCh. 19.2 - A 15-lb slender rod AB is riveted to a 12-lb...Ch. 19.2 - A 20-lb uniform cylinder can roll without sliding...Ch. 19.2 - A square plate of mass m is held by eight springs,...Ch. 19.2 - Prob. 19.44PCh. 19.2 - Prob. 19.45PCh. 19.2 - A three-blade wind turbine used for research is...Ch. 19.2 - A connecting rod is supported by a knife-edge at...Ch. 19.2 - A semicircular hole is cut in a uniform square...Ch. 19.2 - A uniform disk of radius r = 250 mm is attached at...Ch. 19.2 - A small collar of mass 1 kg is rigidly attached to...Ch. 19.2 - Prob. 19.51PCh. 19.2 - Prob. 19.52PCh. 19.2 - Prob. 19.53PCh. 19.2 - Prob. 19.54PCh. 19.2 - The 8-kg uniform bar AB is hinged at C and is...Ch. 19.2 - Prob. 19.56PCh. 19.2 - Prob. 19.57PCh. 19.2 - Prob. 19.58PCh. 19.2 - Prob. 19.59PCh. 19.2 - Prob. 19.60PCh. 19.2 - Two uniform rods, each of weight W = 24 lb and...Ch. 19.2 - A homogeneous rod of mass per unit length equal to...Ch. 19.2 - Prob. 19.63PCh. 19.2 - Prob. 19.64PCh. 19.2 - A 60-kg uniform circular plate is welded to two...Ch. 19.2 - Prob. 19.66PCh. 19.2 - Prob. 19.67PCh. 19.2 - The centroidal radius of gyration ky of an...Ch. 19.3 - Two blocks each have a mass 1.5 kg and are...Ch. 19.3 - Prob. 19.70PCh. 19.3 - Prob. 19.71PCh. 19.3 - Prob. 19.72PCh. 19.3 - Prob. 19.73PCh. 19.3 - Prob. 19.74PCh. 19.3 - Prob. 19.75PCh. 19.3 - Prob. 19.76PCh. 19.3 - Prob. 19.77PCh. 19.3 - Blade AB of the experimental wind-turbine...Ch. 19.3 - A 15-lb uniform cylinder can roll without sliding...Ch. 19.3 - Prob. 19.80PCh. 19.3 - Prob. 19.81PCh. 19.3 - Prob. 19.82PCh. 19.3 - Prob. 19.83PCh. 19.3 - Prob. 19.84PCh. 19.3 - A homogeneous rod of weight W and length 2l is...Ch. 19.3 - A 10-lb uniform rod CD is welded at C to a shaft...Ch. 19.3 - Prob. 19.87PCh. 19.3 - Prob. 19.88PCh. 19.3 - Prob. 19.89PCh. 19.3 - Prob. 19.90PCh. 19.3 - Prob. 19.91PCh. 19.3 - Prob. 19.92PCh. 19.3 - Prob. 19.93PCh. 19.3 - A uniform rod of length L is supported by a...Ch. 19.3 - Prob. 19.95PCh. 19.3 - Three collars each have a mass m and are connected...Ch. 19.3 - Prob. 19.97PCh. 19.3 - As a submerged body moves through a fluid, the...Ch. 19.4 - A 4-kg collar can slide on a frictionless...Ch. 19.4 - Prob. 19.100PCh. 19.4 - A collar with mass m that slides on a frictionless...Ch. 19.4 - Prob. 19.102PCh. 19.4 - The 1.2-kg bob of a simple pendulum of length l =...Ch. 19.4 - Prob. 19.104PCh. 19.4 - A precision experiment sits on an optical table...Ch. 19.4 - Prob. 19.106PCh. 19.4 - Prob. 19.107PCh. 19.4 - The crude-oil pumping rig shown is driven at 20...Ch. 19.4 - Prob. 19.109PCh. 19.4 - Prob. 19.110PCh. 19.4 - Prob. 19.111PCh. 19.4 - Rod AB is rigidly attached to the frame of a motor...Ch. 19.4 - Prob. 19.113PCh. 19.4 - Prob. 19.114PCh. 19.4 - A motor of weight 100 lb is supported by four...Ch. 19.4 - Prob. 19.116PCh. 19.4 - Prob. 19.117PCh. 19.4 - Prob. 19.118PCh. 19.4 - Prob. 19.119PCh. 19.4 - One of the tail rotor blades of a helicopter has...Ch. 19.4 - Prob. 19.121PCh. 19.4 - Prob. 19.122PCh. 19.4 - Prob. 19.123PCh. 19.4 - Prob. 19.124PCh. 19.4 - A 60-lb disk is attached with an eccentricity e =...Ch. 19.4 - A small trailer and its load have a total mass of...Ch. 19.5 - Prob. 19.127PCh. 19.5 - Prob. 19.128PCh. 19.5 - Prob. 19.129PCh. 19.5 - Prob. 19.130PCh. 19.5 - Prob. 19.131PCh. 19.5 - Prob. 19.132PCh. 19.5 - Prob. 19.133PCh. 19.5 - Prob. 19.134PCh. 19.5 - Prob. 19.135PCh. 19.5 - Prob. 19.136PCh. 19.5 - Prob. 19.137PCh. 19.5 - Prob. 19.138PCh. 19.5 - A machine element weighing 500 lb is supported by...Ch. 19.5 - Prob. 19.140PCh. 19.5 - Prob. 19.141PCh. 19.5 - Prob. 19.142PCh. 19.5 - Prob. 19.143PCh. 19.5 - A 36-lb motor is bolted to a light horizontal beam...Ch. 19.5 - One of the tail rotor blades of a helicopter has...Ch. 19.5 - Prob. 19.146PCh. 19.5 - Prob. 19.147PCh. 19.5 - Prob. 19.148PCh. 19.5 - Prob. 19.149PCh. 19.5 - Prob. 19.150PCh. 19.5 - The suspension of an automobile can be...Ch. 19.5 - Prob. 19.152PCh. 19.5 - Prob. 19.153PCh. 19.5 - Prob. 19.154PCh. 19.5 - 19.155 and 19.156 Draw the electrical analog of...Ch. 19.5 - Prob. 19.156PCh. 19.5 - 19.157 and 19.158Write the differential equations...Ch. 19.5 - 19.157 and 19.158Write the differential equations...Ch. 19 - An automobile wheel-and-tire assembly of total...Ch. 19 - Prob. 19.160RPCh. 19 - Disks A and B weigh 30 lb and 12 lb, respectively,...Ch. 19 - A small trailer and its load have a total mass of...Ch. 19 - A 0.8-lb ball is connected to a paddle by means of...Ch. 19 - Prob. 19.164RPCh. 19 - A 4-lb uniform rod is supported by a pin at O and...Ch. 19 - Prob. 19.166RPCh. 19 - Prob. 19.167RPCh. 19 - A small ball of mass m attached at the midpoint of...Ch. 19 - Prob. 19.169RPCh. 19 - If either a simple or a compound pendulum is used...
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
- 3. A particle of mass m is at rest at the end of the spring (force constant k) hanging from a fixed support. At t=0, a constant downward force F is applied to the mass and acts for a time to. Show that after the force is removed, the displacement of the mass from its equilibrium position (x=xo, where x is down) is F -[cos @, (t-t,)- cos w,t] k x- X, where w = k / m.arrow_forwardA car skidded off an icy road and became stuck in deep snow at the road shoulder. Another car, of 1400 kg mass, attempted to jerk the stuck vehicle back onto the road using a 5 m steel tow cable of stiffness k = 5000 N/mm. The traction available to the rescue car prevented it from exerting any significant force on the cable. With the aid of a push from bystanders, the rescue car was able to back against the stuck car and then go forward and reach a speed of 4 km/h at the instant the cable became taut. If the cable is attached rigidly to the masses of the cars, estimate the maximum impact force that can be developed in the cable, and the resulting cable elongation. Assume that the steady state force, acting on the rope, is equal to the weight of the car.arrow_forward3. A hinged rigid bar of length 1 =3 m (where 12=2.11-2m) is connected by two springs of stiffnesses k1=2K and k2=3K and is subjected to a force F as shown below. Assuming that the angular displacement of the bar 0 is small, determine the equivalent spring constant of the system that relates the applied force F to the resulting displacement x located at point C wwwwww xxxx k₂ 00000 k₁ Tarrow_forward
- A jet engine is attached to the wing of an airplane by a security screw (Figure A, marked in black) with a diameter of 40 mm whose purpose is to ensure that if, following a malfunction, the engine exerts too great a horizontal force F on the wing - the screw will break and the engine will detach from the wing, thus the wing will remain intact It is known that the weight of the engine is 3000 kg. A. When the engine exerts a force F of 10 kn, what types of stresses act on the screw? B. When the engine exerts a force F of 10 kn, what is the stress acting on the screw according to the Tarska criterion C. What types of deformations exist in the material when the engine applies a force F of [50] KN d. What is the maximum force F that the motor can apply to a screw without the screw breakingarrow_forwardAs a submerged body moves through a fluid, the particles of the fluid flow around the body and thus acquire kinetic energy. In the case of a sphere moving in an ideal fluid, the total kinetic energy acquired by the fluid is where p is the mass density of the fluid, V is the volume of the sphere, and v is the velocity of the sphere. Consider a 500-g hollow spherical shell of radius 80 mm that is held submerged in a tank of water by a spring of constant 500 N/m. (a ) Neglecting fluid friction, determine the period of vibration of the shell when it is displaced vertically and then released. (b) Solve part a, assuming that the tank is accelerated upward at the constant rate of 8 m/s2.arrow_forwardA sling shot was released in a vertical direction using a rubber band having an equivalent spring constant of 2N/mm. If the deflection of the rubber band amounts to 10cm and the mass of the stone is 21g, determine the maximum height (above the undeflected position of the sling) the shot can reach.arrow_forward
- Two uniform bars AB and BC are pin-connected at points A, B, and C. Bar AB is massless (mAB = 0 kg) and has a length L = 1.5 m. Bar BC has a mass mBc = 2 kg and a length H = 1 m. C is a fixed point, a distance 8 = 0.2 m above the ground. A is on a uniform wheel of radius R = 0.8 m, a distance p from the center of the wheel. Note that p is less than R (R+ p = 8 + H). The mass of the wheel is mwheel = 6 kg. At the instant shown, AB is horizontal, BC is vertical and point A is at the vertical of point O. Bar BC is rotating clockwise at 3 rad/s with an acceleration of 1.5 rad/s² also in the clockwise direction. Assume that the wheel rolls without slipping. a) Find the force P applied to the wheel at that instant. b) Find the minimum coefficient of static friction required for the wheel to roll without slipping. L B Harrow_forward4G !: 4:49 A sulms.su.edu.om The 0.5 N pellet is pushed against the spring and released from rest at A as shown in the figure below. Neglecting friction, determine the smallest deflection of the spring for which the pellet will travel around the loop and remain in contact with the loop at all times. (Use the principle of energy conservation). D 2 m k = 3 N/cm E W = 0.5 N B А Вr,2011 O a. 1.5 m O b. 1.3 m O c. 0.9 m O d. 1.1 m Clear my choicearrow_forwardThe 33-Mg freight car A and 11-Mg freight car B are moving towards each other with the velocities shown. (Figure 1) Figure 20 km/h k = 3 MN/m 10 km/h am B 1 of 1 Part A Determine the maximum compression of the spring mounted on car A. Neglect rolling resistance. Express your answer to three significant figures and include the appropriate units. View Available Hint(s) Smax = Submit Provide Feedback Value Units 2 ? Review Next >arrow_forward
- 3G lI. 11:35 الهندسي. . . تقرير الميكانيك Engineering Mechanic Write a brief report on the subject of engineering mechanics that was studied in the first course of the academic year 2021-2022, explaining the following topics: 1- When we can consider that the body is completely in equilibrium state in terms of the forces and the moment? 2- If we have a circle, half of this circle made of steel, while the other half made of wood, do you think that the centroid will be the center of this circle itself? 3- Mention if we can ignore the friction phenomena from our life, then do you think it (friction) has any negative effects in the engineering issues? 4- Do you think that you change your impression about the Engineering after studying the Mechanic?arrow_forwardA box with a mass of 3m is on frictionless ground, attached to a wall (on the left-side of the box) by a spring with constant k. Inside the box (on the frictionless floor of the box), is a block of mass m. The block is also attached to the left-side of the box (but inside it), by a second spring, with a spring constant 2k/5.1) What are the F = ma equations for the box and the block? (Remember how the motion of each, affects each other)2) What are the matrices K and M for the system?3) What are the normal frequencies of the system?4) Describe the motion of the masses. In phase? Out of phase? Does one mass oscillate with a higher amplitude than the other?arrow_forwardThe force-deflection relation of a steel helical spring used in an engine is found experimentally as F( x) = 200 x + 50 x2 + 10 x3, where the force (F) and deflection (x) are measured in pounds and inches, respectively. If the spring undergoes a steady deflection of 0.5 in. during the operation of the engine, determine the equivalent linear spring constant of the spring at its steady deflection.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Ch 2 - 2.2.2 Forced Undamped Oscillation; Author: Benjamin Drew;https://www.youtube.com/watch?v=6Tb7Rx-bCWE;License: Standard youtube license