Practice_Exam_3(1)

# Practice_Exam_3(1) - 3 Article 3/4 Problems 157...

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Unformatted text preview: 3 Article 3/4 Problems 157 Representative Problems 3/18 The three-wheel truck is used to carry the 100-kg box as shown. Calculate the changes in the normal force reactions at the three wheels due to the weight of the box. Problem 3/78 3/79 The square steel plate has a mass of 1800 kg with mass center at its center G. Calculate the tension in each of the three cables with which the plate is lifted while remaining horizontal. Problem 3/79 3/80 The two uniform rectangular plates each weighing 800 lb are freely hinged about their common edge and suspended by the central cable and four sym- metrical corner cables. Calculate the tension T in each of the corner cables and the tension To in the center cable. Problem 3/80 3/81 The smooth homogeneous sphere rests in the 120° groove and bears against the end plate, which is normal to the direction of the groove. Determine the angle 0, measured from the horizontal, for which the reaction on each side of the groove equals the force supported by the end plate. / I End view of V-groove - — — — - ~— — Horizontal Problem 3/81 158 Chapter 3 Equilibrium 3/ 82 Because of a combination of soil support conditions 3/84 A smooth homogeneous sphere of mass m and ra- and the tension in the single power cable, the utility pole has developed the indicated 5° lean. The 9-m uniform pole has a mass per unit length of 25 kg/m, and the tension in the power cable is 900 N. Deter- mine the reactions at the base 0. Note that the power cable lies in a vertical plane parallel to the x-z plane. Problem 3/82 3/83 As part of a check on its design, a lower A-arm (part of an automobile suspension) is supported by bear- ings at A and B and subjected to the pair of 900-N forces at C and D. The suspension spring, not shown for clarity, exerts a force FS at E as shown, where E is in plane ABCD. Determine the magnitude FS of the spring force and the magnitudes FA and FE of the bearing forces at A and B which are perpendicu- lar to the hinge axis AB. Problem 3/83 3/85 37” dius r is suspended by a wire AB of length 2r from point B on the line of intersection of the two smooth vertical walls at right angles to one another. Deter- mine the reaction R of each wall against the sphere. Problem 3/84 A rider holds her bicycle at the 10° angle shown by exerting a force perpendicular to the plane of the bi- cycle frame. If friction at A and B is sufﬁcient to prevent lateral slippage, determine the force exerted by the rider on the seat, the upward normal forces at A and B, and the lateral friction forces at A and B. Even though the bicycle is free to roll, assume that it does not. The bicycle weighs 29 lb with cen- ter of gravity at G. Problem 3/85 are. 1 by a bi- t to rted rces and Lime cen- vertical 3/56 The 100-lb uniform square plate is supported by a ball-and-socket joint at O, a cable at E, a ﬁxture at A which can support vertical force only, and a linear Spring at C. If the unstretched length of the spring is 6 in., determine the spring constant k required for equilibrium in the position shown. Problem 3l86 13:] 87 During a test, the left engine of the twin-engine air- plane is revved up and a 2-kN thrust is generated. The main wheels at B and C are braked in order to prevent motion. Determine the change (compared with the nominal values with both engines off) in the normal reaction forces at A, B, and C. Problem 3/87 3/88 The uniform 15-kg plate is welded to the vertical shaft, which is supported by bearings A and B. Calculate the magnitude of the force supported by bearing B during application of the 120-N - m couple to the shaft. The cable from C to D prevents the plate and shaft from turning, and the weight of the assembly is carried entirely by bearing A. Article 3/4 Problems 159 400 mm Problem 3] 88 3I89 The uniform panel door weighs 60 lb and is pre- vented from opening by the strut C, which is a light two-force member whose upper end is secured under the door knob and whose lower end is at- tached to a rubber cup which does not slip on the ﬂoor. Of the door hinges A and B, only B can sup— port force in the vertical z-direction. Calculate the compression C in the strut and the horizontal com- ponents of the forces supported by hinges A and B when a horizontal force P = 50 lb is applied normal to the plane of the door as shown. “x. ___—~'|-. I J _.,,_s_.—~ \ "EX \ \ 3’ Problem 3189 Article 5/7 Problems 289 | \ .— 5,145 The angle strut is welded to the end 0 of the 5] 148 Repeat Prob. 5/147, where the 1500-N load has 9am lent I-beam and supports the 1.6-kN vertical force. been replaced by the 4.2-kN-m couple. Determine the bending moment at B and the dis- tance x to the left of C at which the bending mo- ment is zero. Also construct the moment diagram for the beam. 1.6 kN ,. 200 “ Problem 5114B 5] 149 The adjusting screw of the special-purpose offset clamp supports a compression of 500 N. Calculate the shear force V, the tension T, and the bending moment M at section A of the clamp bar for x = and _ 250 mm. Which of these three quantities changes l and with x? Problem 5] 145 5I'l46 The I-beam supports the 1000-lb force and the 2000-lb-ft couple applied to the 2-ft strut welded to the end of the beam. Calculate the shear V and mo- ment M at the section midway between A and B. 1000 lb 2000 lb-tt Problem 51149 5I150 Draw the shear and moment diagrams for the I. the ' _ _ loaded beam and specify the shear V and moment 5; Strut M at a section 3 m to the left of the support at A. riding 4-.— 3' 44.53- .}.:_3*_,. E i Problem 5]]46 : 5] 147 Plot the shear and moment diagrams for the beam ' . _ ! loaded with both the distributed and point loads. - What are the values of the shear and moment "" at x = 6 m? Determine the maximum bending 4:1 moment Mmﬂx. " 6 m ' ' 3 m 1500 N Problem 5,150 800 N/m ‘— — x Problem 5] 147 352 Chapter 6 Friction 6/34 Determine the range of weights W of the uniform slender bar for which the system will be in equilib- rium. Neglect friction at all bearings. Problem 6l34 6/35 The uniform rod with center of mass at G is sup- ported by the pegs A and B, which are ﬁxed in the wheel. If the coefﬁcient of friction between the rod and pegs is [.L, determine the angle 0 through which the wheel may be slowly turned about its horizontal axis through 0, starting from the position shown, before the rod begins to slip. Neglect the diameter of the rod compared with the other dimensions. Problem 6/35 6/36 The solid semicylinder of mass m and radius r is rolled through an angle 0 by the horizontal force P. If the coefﬁcient of static friction is us, determine the angle 0 at which the cylinder begins to slip on the horizontal surface as P is gradually increased. What value of us would permit 0 to reach 90°? Problem 6136 6/37 The 10-kg solid cylinder is resting in the inclined V-block. If the coefﬁcient of static friction between the cylinder and the block is 0.50, determine (a) the friction force F acting on the cylinder at each side before force P is applied and (b) the value of P required to start sliding the cylinder up the incline. l____ Horiz. — — — Problem 6I37 6/38 The three identical rollers are stacked on a horizon- tal surface as shown. If the coefﬁcient of static friction its is the same for all pairs of contacting sur- faces, ﬁnd the minimum value of us for which the rollers will not slip. Problem 6/38 Article 6/3 Problems 353 ined 6139 The movable left-hand jaw of the bar clamp can be veen slid along the frame to increase the capacity of )the the clamp. To prevent slipping of the jaw on the side frame when the clamp is under load, the dimension of p x must exceed a certain minimum value. For given ine. values of a and b and a static friction coefﬁcient as, specify this design minimum value of x to prevent slipping of the jaw. Problem 6/4'I 6/42 A uniform block of mass m is at rest on an incline 6. Determine the maximum force P which can be ap- plied to the block in the direction shown before P slipping begins. The coefﬁcient of static friction between the block and the incline is us. Also deter- mine the angle B between the horizontal direction of P and the direction of initial movement of the block. Problem 6I39 izon- itatic 6I40 The uniform slender bar of length l is placed in the _ sup opening of width d at the 30° angle shown. For what '1 the range of l/d will the bar remain in static equilib- rium? The coefﬁcient of static friction at A and B is as = 0.40. Problem 6I42 6/43 The single-lever block brake prevents rotation of the ﬂywheel under a counterclockwise torque M. Find the force P required to prevent rotation if the coefﬁcient of static friction is as. Explain what would happen if the geometry permitted b to equal use. Problem 6/40 6I41 Determine the maximum value of the angle 0 for which the uniform slender rod will remain in equi- librium. The coefﬁcient of static friction at A is “A = 0.80, and friction associated with the small roller at B may be neglected. Problem 6143 ...
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## This note was uploaded on 12/15/2011 for the course EM 306 taught by Professor Rodin during the Fall '07 term at University of Texas.

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Practice_Exam_3(1) - 3 Article 3/4 Problems 157...

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