INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
14th Edition
ISBN: 9780133918922
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 8.2, Problem 4P
The winch on the truck is used to hoist the garbage bin onto the bed of the truck. If the loaded bin has a weight of 8500 lb and center of gravity at G, determine the force in the cable needed to begin the lift. The coefficients of static friction at A and B are, μA = 0.3 and, μB = 0.2, respectively. Neglect the height of the support at A.
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An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
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Mechanical engineering
Chapter 8 Solutions
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
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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