Engineering Mechanics: Statics Plus Mastering Engineering with Pearson eText -- Access Card Package (14th Edition) (Hibbeler, The Engineering Mechanics: Statics & Dynamics Series, 14th Edition)
14th Edition
ISBN: 9780134160689
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 8.2, Problem 20P
The ring has a mass of 0.5 kg and is resting on the surface of the table. In an effort to move the ring a normal force P from the finger is exerted on it. If this force is directed towards the ring’s center O as shown, determine its magnitude when the ring is on the verge of slipping at A. The coefficient of static friction at A is, μA = 0.2 and at B, μB = 0.3.
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
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Chapter 8 Solutions
Engineering Mechanics: Statics Plus Mastering Engineering with Pearson eText -- Access Card Package (14th Edition) (Hibbeler, The Engineering Mechanics: Statics & Dynamics Series, 14th Edition)
Ch. 8.2 - Determine the friction force at the surface of...Ch. 8.2 - Determine M to cause impending motion of the...Ch. 8.2 - Determine the force P to move block B.Ch. 8.2 - Determine the force P needed to cause impending...Ch. 8.2 - Determine the friction developed between the 50-kg...Ch. 8.2 - Determine the minimum force P to prevent the 30-kg...Ch. 8.2 - Determine the maximum force P that can be applied...Ch. 8.2 - If the coefficient of static friction at contact...Ch. 8.2 - Determine the maximum force P that can be applied...Ch. 8.2 - Prob. 6FP
Ch. 8.2 - Blocks A, B, and C have weights of 50 N, 25 N, and...Ch. 8.2 - If the coefficient of static friction at all...Ch. 8.2 - Using the coefficients of static friction...Ch. 8.2 - Determine the maximum force P the connection can...Ch. 8.2 - The tractor exerts a towing force T=400 lb....Ch. 8.2 - Prob. 3PCh. 8.2 - The winch on the truck is used to hoist the...Ch. 8.2 - The automobile has a mass of 2 Mg and center of...Ch. 8.2 - The automobile has a mass of 2 Mg and canter of...Ch. 8.2 - The block brake consists of a pin-connected lever...Ch. 8.2 - The block brake consists of a pin-connected lever...Ch. 8.2 - Prob. 9PCh. 8.2 - Prob. 10PCh. 8.2 - Determine the maximum weight W the man can lift...Ch. 8.2 - The block brake is used to stop the wheel from...Ch. 8.2 - If a torque of M=300 Nm is applied to the...Ch. 8.2 - The car has a mass of 1.6 Mg and center of mass at...Ch. 8.2 - Prob. 15PCh. 8.2 - The 180-Ib man climbs up the ladder and stops at...Ch. 8.2 - The 180-Ib man climbs up the ladder and stops at...Ch. 8.2 - The spool of wire having a weight of 300 Ib rests...Ch. 8.2 - Prob. 19PCh. 8.2 - The ring has a mass of 0.5 kg and is resting on...Ch. 8.2 - A man attempts to support a stack of books...Ch. 8.2 - The tongs are used to lift the 150-kg crate, whose...Ch. 8.2 - The beam is supported by a pin at A and a roller...Ch. 8.2 - The uniform thin pole has a weight of 30 Ib and a...Ch. 8.2 - The uniform pole has a weight of 30 Ib and a...Ch. 8.2 - The block brake is used to stop the wheel from...Ch. 8.2 - Solve Prob. 8-26 if the couple moment M0 is...Ch. 8.2 - A worker walks up the sloped roof that is defined...Ch. 8.2 - Prob. 29PCh. 8.2 - Two blocks A and B have a weight of 10 Ib and 6...Ch. 8.2 - Two blocks A and B have a weight of 10 Ib and 6...Ch. 8.2 - Determine the smallest force P that must be...Ch. 8.2 - The man having a weight of 200 Ib pushes...Ch. 8.2 - The uniform hoop of weight W is subjected to the...Ch. 8.2 - Prob. 35PCh. 8.2 - Determine the minimum force P needed to push the...Ch. 8.2 - Prob. 37PCh. 8.2 - The coefficient of static friction between the...Ch. 8.2 - Determine the smallest coefficient of static...Ch. 8.2 - Prob. 40PCh. 8.2 - If the coefficient of static friction at A and B...Ch. 8.2 - The 100-kg disk rests on a surface for which, B =...Ch. 8.2 - Investigate whether the equilibrium can be...Ch. 8.2 - Prob. 44PCh. 8.2 - The beam AB has a negligible mass and thickness...Ch. 8.2 - It is supported at one end by a pin and at the...Ch. 8.2 - Crates A and B weigh 200 Ib and 150 Ib,...Ch. 8.2 - Two blocks A and B, each having a mass of 5 kg,...Ch. 8.2 - The uniform crate has a mass of 150 kg. If the...Ch. 8.2 - The uniform crate has a mass of 150 kg. If the...Ch. 8.2 - Beam AB has a negligible mass and thickness, and...Ch. 8.2 - Beam AB has a negligible mass and thickness, and...Ch. 8.2 - Determine the smallest couple moment that can be...Ch. 8.2 - Determine the greatest angle so that the ladder...Ch. 8.2 - The wheel weights 20 lb and rests on a surface for...Ch. 8.2 - Prob. 56PCh. 8.2 - The man has a weight of 200 lb, and the...Ch. 8.2 - Prob. 1CPCh. 8.2 - Prob. 4CPCh. 8.2 - Explain how to find the maximum force this man can...Ch. 8.4 - Determine the largest angle that will cause the...Ch. 8.4 - If the beam AD is loaded as shown, determine the...Ch. 8.4 - The wedge is used to level the member. Determine...Ch. 8.4 - Prob. 61PCh. 8.4 - If P=250 N, determine the required minimum...Ch. 8.4 - Determine the minimum applied force P required to...Ch. 8.4 - If the coefficient of static friction between all...Ch. 8.4 - Determine the smallest force P needed to lift the...Ch. 8.4 - Prob. 66PCh. 8.4 - If the clamping force at G is 900 N, determine the...Ch. 8.4 - If a horizontal force of F = 50 N is applied...Ch. 8.4 - Prob. 69PCh. 8.4 - If the force F is removed from the handle of the...Ch. 8.4 - Prob. 71PCh. 8.4 - If the clamping force on the boards is 600 lb,...Ch. 8.4 - Prob. 73PCh. 8.4 - The square-threaded bolt is used to join two...Ch. 8.4 - The shaft has a square-threaded screw with a lead...Ch. 8.4 - If couple forces of F=35 N are applied to the...Ch. 8.4 - Prob. 77PCh. 8.4 - The device is used to pull the battery cable...Ch. 8.4 - Determine the clamping force on the board A if the...Ch. 8.4 - If the required clamping force on the board A is...Ch. 8.4 - If a horizontal force of P = 100 N is applied...Ch. 8.4 - Determine the horizontal force P that must be...Ch. 8.5 - A cylinder having a mass of 250 kg is to be...Ch. 8.5 - A cylinder having a mass of 250 kg is to be...Ch. 8.5 - A 180-lb farmer tries to restrain the cow from...Ch. 8.5 - The 100-lb boy at A is suspended from the cable...Ch. 8.5 - The 100-lb boy at A is suspended from the cable...Ch. 8.5 - Prob. 88PCh. 8.5 - A cable is attached to the 20-kg plate B, passes...Ch. 8.5 - Prob. 90PCh. 8.5 - Prob. 91PCh. 8.5 - Determine the force P that must be applied to the...Ch. 8.5 - Prob. 93PCh. 8.5 - Determine the weight of the cylinder if the...Ch. 8.5 - If slipping does not occur at the wall, determine...Ch. 8.5 - The coefficient of static friction between the...Ch. 8.5 - Prob. 97PCh. 8.5 - Show that the frictional relationship between the...Ch. 8.5 - The wheel is subjected to a torque of M = 50 N m...Ch. 8.5 - Using the coefficients of static friction...Ch. 8.5 - If the coefficient of static friction between the...Ch. 8.5 - Idler pulley A, and motor pulley B. If the motor...Ch. 8.5 - Using the coefficient of static friction...Ch. 8.5 - Determine the smallest counterclockwise twist or...Ch. 8.5 - Determine the largest angles so that the cord...Ch. 8.5 - Determine the smallest stretch of the spring...Ch. 8.8 - If the coefficient of static is, s = 0.3,...Ch. 8.8 - Prob. 108PCh. 8.8 - Prob. 109PCh. 8.8 - Prob. 110PCh. 8.8 - Prob. 111PCh. 8.8 - Prob. 113PCh. 8.8 - Prob. 114PCh. 8.8 - Prob. 115PCh. 8.8 - Prob. 116PCh. 8.8 - Prob. 117PCh. 8.8 - If the coefficient of static friction is. k....Ch. 8.8 - If the coefficient of static friction between the...Ch. 8.8 - If the coefficient of kinetic friction between the...Ch. 8.8 - if the force P is applied horizontally to the...Ch. 8.8 - Prob. 122PCh. 8.8 - Prob. 123PCh. 8.8 - Prob. 124PCh. 8.8 - Prob. 125PCh. 8.8 - The bell crank fits loosely into a 0.5-in-diameter...Ch. 8.8 - Prob. 127PCh. 8.8 - The vehicle has a weight of 2600 lb and center of...Ch. 8.8 - The tractor has a weight of 16 000 lb and the...Ch. 8.8 - Prob. 130PCh. 8.8 - Prob. 131PCh. 8.8 - The 1.4-Mg machine is to be moved over a level...Ch. 8.8 - Prob. 1RPCh. 8.8 - The uniform 60-kg crate C rests uniformly on a...Ch. 8.8 - A 35-kg disk rests on an inclined surface for...Ch. 8.8 - The cam is subjected to a couple moment of 5N m....Ch. 8.8 - The three stone blocks have weights of, WA =...Ch. 8.8 - Prob. 6RPCh. 8.8 - Prob. 7RPCh. 8.8 - Prob. 8RP
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- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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