3D_Equilibrium_WileyPlus

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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 1/59 CHAPTER 3 Equilibrium Chapter 3 Problems Computer-oriented problem Difficult problem Problems for Article 3/3 Introductory Problems 3/1 The 50-kg homogeneous smooth sphere rests on the 30° incline A and bears against the smooth vertical wall B . Calculate the contact forces at A and B . 3/2 The mass center G of the 1400-kg rear-engine car is located as shown in the figure. Determine the normal force under each tire when the car is in equilibrium. State any assumptions. 3/3 A carpenter holds a 12-lb 2-in. by 4-in. board as shown. If he exerts vertical forces on the board, determine the forces at A and B .
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 2/59 Video Solution: Problem 3/3 3/4 The 450-kg uniform I-beam supports the load shown. Determine the reactions at the supports. 3/5 Determine the force P required to maintain the 200-kg engine in the position for which θ = 30°. The diameter of the pulley at B is negligible.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 3/59 3/6 The uniform 15-m pole has a mass of 150 kg and is supported by its smooth ends against the vertical walls and by the tension T in the vertical cable. Compute the reactions at A and B . 3/7 Determine the reactions at A and E if P = 500 N. What is the maximum value which P may have for static equilibrium? Neglect the weight of the structure compared with the applied loads.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 4/59 3/8 A 120-lb crate rests on the 60-lb pickup tailgate. Calculate the tension T in each of the two restraining cables, one of which is shown. The centers of gravity are at G 1 and G 2 . The crate is located midway between the two cables. Video Solution: Problem 3/8 3/9 The 20-kg uniform rectangular plate is supported by an ideal pivot at O and a spring which must be compressed prior to being slipped into place at point A . If the modulus of the spring is k = 2 kN/m, what must be its undeformed length L ?
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 5/59 3/10 The 500-kg uniform beam is subjected to the three external loads shown. Compute the reactions at the support point O . The x - y plane is vertical. 3/11 A former student of mechanics wishes to weigh himself but has access only to a scale A with capacity limited to 100 lb and a small 20-lb spring dynamometer B . With the rig shown he discovers that when he exerts a pull on the rope so that B registers 19 lb, the scale A reads 67 lb. What is his correct weight?
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 6/59 3/12 To facilitate shifting the position of a lifting hook when it is not under load, the sliding hanger shown is used. The projections at A and B engage the flanges of a box beam when a load is supported, and the hook projects through a horizontal slot in the beam. Compute the forces at A and B when the hook supports a 300-kg mass. 3/13 What weight W B will cause the system to be in equilibrium? Neglect all friction, and state any other assumptions.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 7/59 Video Solution: Problem 3/13 3/14 The wall-mounted 2.5-kg light fixture has its mass center at G . Determine the reactions at A and B and also calculate the moment supported by the adjustment thumbscrew at C . (Note that the lightweight frame ABC has about 250 mm of horizontal tubing, directed into and out of the paper, at both A and B .) 3/15 The winch takes in cable at the constant rate of 200 mm/s. If the cylinder mass is 100 kg, determine the tension in cable 1. Neglect all friction.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 8/59 3/16 To accommodate the rise and fall of the tide, a walkway from a pier to a float is supported by two rollers as shown. If the center of gravity of the 600-lb walkway is at G , calculate the tension T in the horizontal cable which is attached to the cleat and find the force under the roller at A . 3/17 When the 0.05-kg body is in the position shown, the linear spring is stretched 10 mm. Determine the force P required to break contact at C . Complete solutions for ( a ) including the effect of the weight and ( b ) neglecting the weight.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 9/59 3/18 When the 0.05-kg body is in the position shown, the torsional spring at O is pretensioned so as to exert a 0.75-N · m clockwise moment on the body. Determine the force P required to break contact at C . Complete solutions for ( a ) including the effect of the weight and ( b ) neglecting the weight. 3/19 When on level ground, the car is placed on four individual scales—one under each tire. The scale readings are 4450 N at each front wheel and 2950 N at each rear wheel. Determine the x - coordinate of the mass center G and the mass of the car.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 10/59 3/20 Determine the magnitude P of the force required to rotate the release pawl OB counterclockwise from its locked position. The torsional spring constant is k T = 3.4 N · m/rad and the pawl end of the spring has been deflected 25° counterclockwise from the neutral position in the configuration shown. Neglect any forces at the contact point B . 3/21 The 180-lb exerciser is beginning to execute some slow, steady bicep curls. As the tension T = 15 lb is developed against an exercise machine (not shown), determine the normal reaction forces at the feet A and B . Friction is sufficient to prevent slipping, and the exerciser maintains the position shown with center of gravity at G .
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 11/59 3/22 The force P on the handle of the positioning lever produces a vertical compression of 60 lb in the coiled spring in the position shown. Determine the corresponding force exerted by the pin at O on the lever.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 12/59 Video Solution: Problem 3/22 3/23 Determine the moment M which the motor must exert in order to position the uniform slender bar of mass m and length L in the arbitrary position θ . The ratio of the radius of the gear wheel B attached to the bar to that of the gear wheel A attached to the motor shaft is 2. 3/24 A bicyclist applies a 40-N force to the brake lever of her bicycle as shown. Determine the corresponding tension T transmitted to the brake cable. Neglect friction at the pivot O .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 13/59 Representative Problems 3/25 Find the angle of tilt θ with the horizontal so that the contact force at B will be one-half that at A for the smooth cylinder. 3/26 The rack has a mass m = 75 kg. What moment M must be exerted on the gear wheel by the motor in order to lower the rack at a slow steady speed down the 60° incline? Neglect all friction. The fixed motor which drives the gear wheel via the shaft at O is not shown.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 14/59 Video Solution: Problem 3/26 3/27 The elements of a wheel-height adjuster for a lawn mower are shown. The wheel (partial outline shown dashed for clarity) bolts through the hole at A , which goes through the bracket but not the housing H . A pin fixed to the back of the bracket at B fits into one of the seven elongated holes of the housing. For the position shown, determine the force at the pin B and the magnitude of the reaction at the pivot O . The wheel supports a force of magnitude W /4, where W is the weight of the entire mower.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 15/59 3/28 Cable AB passes over the small ideal pulley C without a change in its tension. What length of cable CD is required for static equilibrium in the position shown? What is the tension T in cable CD ? 3/29 A pipe P is being bent by the pipe bender as shown. If the hydraulic cylinder applies a force of magnitude F = 24 kN to the pipe at C , determine the magnitude of the roller reactions at A and B . 3/30 The asymmetric simple truss is loaded as shown. Determine the reactions at A and D . Neglect the weight of the structure compared with the applied loads. Is knowledge of the size of the structure necessary?
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 16/59 3/31 The indicated location of the center of gravity of the 3600-lb pickup truck is for the unladen condition. If a load whose center of gravity is x = 16 in. behind the rear axle is added to the truck, determine the load weight W L for which the normal forces under the front and rear wheels are equal. 3/32 A uniform ring of mass m and radius r carries an eccentric mass m 0 at a radius b and is in an equilibrium position on the incline, which makes an angle α with the horizontal. If the contacting surfaces are rough enough to prevent slipping, write the expression for the angle θ which defines the equilibrium position.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 17/59 3/33 Determine the force T required to hold the uniform bar of mass m and length L in an arbitrary angular position θ . Plot your result over the range 0 ≤ θ ≤ 90°, and state the value of T for θ = 40°. 3/34 A block placed under the head of the claw hammer as shown greatly facilitates the extraction of the nail. If a 50-lb pull on the handle is required to pull the nail, calculate the tension T in the nail and the magnitude A of the force exerted by the hammer head on the block. The contacting surfaces at A are sufficiently rough to prevent slipping.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 18/59 3/35 The chain binder is used to secure loads of logs, lumber, pipe, and the like. If the tension T 1 is 2 kN when θ = 30°, determine the force P required on the lever and the corresponding tension T 2 for this position. Assume that the surface under A is perfectly smooth. Video Solution: Problem 3/35 3/36 In a procedure to evaluate the strength of the triceps muscle, a person pushes down on a load cell with the palm of his hand as indicated in the figure. If the load-cell reading is 160 N, determine the vertical tensile force F generated by the triceps muscle. The mass of the lower arm is 1.5 kg with mass center at G . State any assumptions.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 19/59 3/37 In sailing at a constant speed with the wind, the sailboat is driven by a 1000-lb force against its mainsail and a 400-lb force against its staysail as shown. The total resistance due to fluid friction through the water is the force R . Determine the resultant of the lateral forces perpendicular to motion applied to the hull by the water. 3/38 A person is performing slow arm curls with a 10-kg weight as indicated in the figure. The brachialis muscle group (consisting of the biceps and brachialis muscles) is the major factor in this exercise. Determine the magnitude F of the brachialis-muscle-group force and the magnitude E of the elbow joint reaction at point E for the forearm position shown in the figure. Take the dimensions shown to locate the effective points of application of the two muscle groups; these points are 200 mm directly above E and 50 mm directly to the right of E . Include the effect of the 1.5-kg forearm mass with mass center at point G . State any assumptions.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 20/59 3/39 The exercise machine is designed with a lightweight cart which is mounted on small rollers so that it is free to move along the inclined ramp. Two cables are attached to the cart—one for each hand. If the hands are together so that the cables are parallel, determine the force P which each hand must exert on its cable in order to maintain an equilibrium position. The mass of the person is 70 kg, the ramp angle θ is 15°, and the angle β is 18°. In addition, calculate the force R which the ramp exerts on the cart. 3/40 The uniform bar OC of length L pivots freely about a horizontal axis through O . If the spring of modulus k is unstretched when C is coincident with A , determine the tension T required to hold the bar in the 45° position shown. The diameter of the small pulley at D is negligible.
12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 21/59 3/41 The device shown is used to test automobile-engine valve springs. The torque wrench is directly connected to arm OB . The specification for the automotive intake-valve spring is that 83 lb of force should reduce its length from 2 in. (unstressed length) to 1 11 16 in. What is the corresponding reading M on the torque wrench, and what force F exerted on the torque-wrench handle is required to produce this reading? Neglect the small effects of changes in the angular position of arm OB .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 22/59 3/42 The portable floor crane in the automotive shop is lifting a 420-lb engine. For the position shown compute the magnitude of the force supported by the pin at C and the oil pressure p against the 3.20-in.-diameter piston of the hydraulic-cylinder unit AB . Video Solution: Problem 3/42 3/43 The torsional spring of constant k T = 50 N · m/rad is undeformed when θ = 0. Determine the value(s) of θ over the range 0 ≤ θ ≤ 180° for which equilibrium exists. Use the values m A = 10 kg, m B = 1 kg, m OA = 5 kg, and r = 0.8 m. Assume that OA is a uniform slender rod with a particle A (negligible size) at its end, and neglect the effects of the small ideal rollers.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 23/59 3/44 A torque (moment) of 24 N · m is required to turn the bolt about its axis. Determine P and the forces between the smooth hardened jaws of the wrench and the corners A and B of the hexagonal head. Assume that the wrench fits easily on the bolt so that contact is made at corners A and B only. 3/45 During an engine test on the ground, a propeller thrust T = 3000 N is generated on the 1800-kg airplane with mass center at G . The main wheels at B are locked and do not skid; the small tail wheel at A has no brake. Compute the percent change n in the normal forces at A and B as compared with their “engine-off” values. 3/46 To test the deflection of the uniform 200-lb beam the 120-lb boy exerts a pull of 40 lb on the rope rigged as shown. Compute the force supported by the pin at the hinge O .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 24/59 3/47 A portion of the shifter mechanism for a manual car transmission is shown in the figure. For the 8-N force exerted on the shift knob, determine the corresponding force P exerted by the shift link BC on the transmission (not shown). Neglect friction in the ball-and-socket joint at O , in the joint at B , and in the slip tube near support D . Note that a soft rubber bushing at D allows the slip tube to self-align with link BC . 3/48 The cargo door for an airplane of circular fuselage section consists of the uniform semicircular cowling AB of mass m . Determine the compression C in the horizontal strut at B to hold the door open in the position shown. Also find an expression for the total force supported by the hinge at A . (Consult Table D/3 of Appendix D for the position of the centroid or mass center of the cowling.)
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 25/59 3/49 It is desired that a person be able to begin closing the van hatch from the open position shown with a 10-lb vertical force P . As a design exercise, determine the necessary force in each of the two hydraulic struts AB . The center of gravity of the 90-lb door is 1.5 in. directly below point A . Treat the problem as two-dimensional. 3/50 Certain elements of an in-refrigerator ice-cube maker are shown in the figure. (A “cube” has the form of a cylindrical segment!) Once the cube freezes and a small heater (not shown) forms a thin film of water between the cube and supporting surface, a motor rotates the ejector arm OA to remove the cube. If there are eight cubes and eight arms, determine the required torque M as a function of θ . The mass of eight cubes is 0.25 kg, and the center-of-mass distance ¯ 𝑟 = 0.55𝑟 . Neglect friction, and assume that the resultant of the distributed normal force acting on the cube passes through point O .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 26/59 3/51 The lumbar portion of the human spine supports the entire weight of the upper torso and the force load imposed on it. We consider here the disk (shaded red) between the lowest vertebra of the lumbar region ( L 5 ) and the uppermost vertebra of the sacrum region. (a) For the case L = 0, determine the compressive force C and the shear force S supported by this disk in terms of the body weight W . The weight W u of the upper torso (above the disk in question) is 68% of the total body weight W and acts at G 1 . The vertical force F which the rectus muscles of the back exert on the upper torso acts as shown in the figure. (b) Repeat for the case when the person holds a weight of magnitude L = W /3 as shown. State any assumptions.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 27/59 3/52 Determine and plot the moment M which much be applied to the crank OA in order to hold the cylinder of mass m = 5 kg in equilibrium. Neglect the effects of the mass of OA and friction and consider the range 0 ≤ θ ≤ 180°. State the maximum and minimum values of the absolute value of M and the values of θ for which these extremes occur, and physically justify these results. Problems for Article 3/4 Introductory Problems 3/53 A uniform steel plate 18 in. square weighing 68 lb is suspended in the horizontal plane by the three vertical wires as shown. Calculate the tension in each wire.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 28/59 3/54 The horizontal steel shaft has a mass of 480 kg and is suspended by a vertical cable from A and by a second cable BC which lies in a vertical transverse plane and loops underneath the shaft. Calculate the tensions T 1 and T 2 in the cables. 3/55 Determine the tensions in cables AB , AC , and AD .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 29/59 Video Solution: Problem 3/55 3/56 An 80-lb sheet of plywood rests on two small wooden blocks as shown. It is allowed to lean 20° from the vertical under the action of a force P which is perpendicular to the sheet. Friction at all surfaces of blocks A and B is sufficient to prevent slipping. Determine the magnitude P and the vertical reaction forces at A and B . 3/57 The vertical and horizontal poles at the traffic-light assembly are erected first. Determine the additional force and moment reactions at the base O caused by the addition of the three 100- lb traffic signals B , C , and D . Report your answers as a force magnitude and a moment magnitude.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 30/59 3/58 In order to make an adjustment, engineering students remove leg D from a laboratory worktable. To ensure that the table remains stable, they place a 6-kg stack of statics textbooks centered at point E of the tabletop as shown. Determine the normal reaction force at each leg A , B , and C . The uniform tabletop has a mass of 40 kg, and each leg has a mass of 5 kg. 3/59 The vertical mast supports the 4-kN force and is constrained by the two fixed cables BC and BD and by a ball-and-socket connection at A . Calculate the tension T 1 in BD . Can this be accomplished by using only one equation of equilibrium?
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 31/59 3/60 An overhead view of a car is shown in the figure. Two different locations C and D are considered for a single jack. In each case, the entire right side of the car is lifted just off the ground. Determine the normal reaction forces at A and B and the vertical jacking force required for the case of each jacking location. Consider the 1600-kg car to be rigid. The mass center G is on the midline of the car. 3/61 The uniform rectangular plate of mass m is suspended by three cables. Determine the tension in each cable.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 32/59 3/62 A smooth homogeneous sphere of mass m and radius r is suspended by a wire AB of length 2 r from point B on the line of intersection of the two smooth vertical walls at right angles to one another. Determine the reaction R of each wall against the sphere. 3/63 A uniform steel ring 60 in. in diameter and weighing 600 lb is lifted by the three cables, each 50 in. long, attached at points A , B , and C as shown. Compute the tension in each cable.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 33/59 3/64 One of the vertical walls supporting end B of the 200-kg uniform shaft of Sample Problem 3/5 is turned through a 30° angle as shown here. End A is still supported by the ball-and-socket connection in the horizontal x - y plane. Calculate the magnitudes of the forces P and R exerted on the ball end B of the shaft by the vertical walls C and D , respectively. Video Solution: Problem 3/64 3/65 The light right-angle boom which supports the 400-kg cylinder is supported by three cables and a ball-and-socket joint at O attached to the vertical x - y surface. Determine the reactions at O and the cable tensions.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 34/59 3/66 The mass center of the 60-lb door is in the center of the panel. If the weight of the door is supported entirely by the lower hinge A , calculate the magnitude of the total force supported by the hinge at B .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 35/59 3/67 The two I-beams are welded together and are initially supported by the three cables of equal length hanging vertically from supports directly above A , B , and C . When applied with the appropriate offset d , the 200-N force causes the system to assume the new equilibrium configuration shown. All three cables are inclined at the same angle θ from the vertical, in planes parallel to the y - z plane. Determine this deflection θ and the proper offset d . Beams AB and OC have masses of 72 kg and 50 kg, respectively. The mass center of beam OC has a y -coordinate of 725 mm. 3/68 The 50-kg uniform triangular plate is supported by two small hinges A and B and the cable system shown. For the horizontal position of the plate, determine all hinge reactions and the tension T in the cable. Hinge A can resist axial thrust, but hinge B cannot. See Table D/3 in Appendix D for the mass-center location of a triangular plate.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 36/59 3/69 The large bracket is constructed of heavy plate which has a mass ρ per unit area. Determine the force and moment reactions at the support bolt at O . Representative Problems 3/70 The 800-lb tree trunk is known to have insect damage near point O , so the winch arrangement shown is used to fell the tree with no cutting. If winch W 1 is tightened to 200 lb and winch W 2 to 300 lb, determine the force and moment reactions at O . If the tree ultimately falls at this point because of the moment at O , determine the angle θ which characterizes the line of impact OE . Assume that the base of the tree is equally strong in all directions. Video Solution: Problem 3/70 3/71 One of the three landing pads for a proposed Mars lander is shown in the figure. As part of a design check on the distribution of force in the landing struts, compute the force in each of the struts AC , BC , and CD when the lander is resting on a horizontal surface on Mars. The
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 37/59 arrangement is symmetrical with respect to the x-z plane. The mass of the lander is 600 kg. (Assume equal support by the pads and consult Table D/2 in Appendix D as needed.) 3/72 Determine the magnitudes of the force R and couple M exerted by the nut and bolt on the loaded bracket at O to maintain equilibrium.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 38/59 3/73 The 50-lb rectangular access door is held in the 90° open position by the single prop CD . Determine the force F in the prop and the magnitude of the force normal to the hinge axis AB in each of the small hinges A and B . 3/74 As part of a check on its design, a lower A-arm (part of an automobile suspension) is supported by bearings 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 F s at E as shown, where E is in plane ABCD . Determine the magnitude F s of the spring force and the magnitudes F A and F B of the bearing forces at A and B which are perpendicular to the hinge axis AB .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 39/59 3/75 The shaft, lever, and handle are welded together and constitute a single rigid body. Their combined mass is 28 kg with mass center at G . The assembly is mounted in bearings A and B , and rotation is prevented by link CD . Determine the forces exerted on the shaft by bearings A and B while the 30-N · m couple is applied to the handle as shown. Would these forces change if the couple were applied to the shaft AB rather than to the handle? 3/76 During a test, the left engine of the twin-engine airplane is revved up and a 500-lb 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 .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 40/59 3/77 The bent rod ACDB is supported by a sleeve at A and a ball-and-socket joint at B . Determine the components of the reactions and the tension in the cable. Neglect the mass of the rod. Video Solution: Problem 3/77
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 41/59 3/78 Turnbuckle T 1 is tightened to a tension of 180 lb and turnbuckle T 2 is tightened to 120 lb. Determine the components of the corresponding force and moment reactions at the built-in support at O . Neglect the weight of the structure. 3/79 The spring of modulus k = 900 N/m is stretched a distance δ = 60 mm when the mechanism is in the position shown. Calculate the force P min required to initiate rotation about the hinge axis BC , and determine the corresponding magnitudes of the bearing forces which are perpendicular to BC . What is the normal reaction force at D if P = P min /2? 3/80 Consider the rudder assembly of a radio-controlled model airplane. For the 15° position shown in the figure, the net pressure acting on the left side of the rectangular rudder area is p =
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 42/59 4(10 −5 ) N/mm 2 . Determine the required force P in the control rod DE and the horizontal components of the reactions at hinges A and B which are parallel to the rudder surface. Assume the aerodynamic pressure to be uniform. 3/81 A rectangular sign over a store has a weight of 250 lb, with the center of gravity in the center of the rectangle. The support against the wall at point C may be treated as a ball-and- socket joint. At corner D support is provided in the y -direction only. Calculate the tensions T 1 and T 2 in the supporting wires, the total force supported at C , and the lateral force R supported at D .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 43/59 3/82 The uniform rectangular panel ABCD has a mass of 40 kg and is hinged at its corners A and B to the fixed vertical surface. A wire from E to D keeps edges BC and AD horizontal. Hinge A can support thrust along the hinge axis AB , whereas hinge B supports force normal to the hinge axis only. Find the tension T in the wire and the magnitude B of the force supported by hinge B . 3/83 The vertical plane containing the utility cable turns 30° at the vertical pole OC . The tensions T 1 and T 2 are both 950 N. In order to prevent long-term leaning of the pole, guy wires AD and BE are utilized. If the two guy wires are adjusted so as to carry equal tensions T which together reduce the moment at O to zero, determine the net horizontal reaction at O . Determine the required value of T . Neglect the weight of the pole.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 44/59 3/84 Determine and plot the moment M required to rotate arm OA over the range 0 ≤ θ ≤ 180°. Find the maximum value of M and the angle θ at which it occurs. The collar C fastened to the shaft prevents downward motion of the shaft in its bearing. Determine and plot the magnitude of the distributed vertical force supported by this collar over the same range of θ . The spring constant k = 200 N/m, and the spring is unstretched when θ = 0. Neglect the mass of the structure and any effects of mechanical interference.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 45/59 Problems for Article 3/5 Chapter Review 3/85 The pin at O can support a maximum force of 3.5 kN. What is the corresponding maximum load L which can be applied to the angled bracket AOB ? 3/86 The light bracket ABC is freely hinged at A and is constrained by the fixed pin in the smooth slot at B . Calculate the magnitude R of the force supported by the pin at A under the action of the 80-N · m applied couple.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 46/59 Video Solution: Problem 3/86 3/87 Determine a general expression for the normal force N A exerted by the smooth vertical wall on the uniform slender bar of mass m and length L . The mass of the cylinder is m 1 , and all bearings are ideal. Determine the value of m 1 which makes ( a ) N A = mg /2 and ( b ) N A = 0. 3/88 The mass of the uniform right-triangular tabletop is 30 kg, and that of each of the vertical legs is 2 kg. Determine the normal reaction force exerted by the floor on each leg. The mass center of a right-triangular body can be obtained from Table D/3 in Appendix D .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 47/59 3/89 The device shown in the figure is useful for lifting drywall panels into position prior to fastening to the stud wall. Estimate the magnitude P of the force required to lift the 25-kg panel. State any assumptions. 3/90 Magnetic tape under a tension of 10 N at D passes around the guide pulleys and through the erasing head at C at constant speed. As a result of a small amount of friction in the bearings of the pulleys, the tape at E is under a tension of 11 N. Determine the tension T in the supporting spring at B . The plate lies in a horizontal plane and is mounted on a precision needle bearing at A .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 48/59 3/91 The tool shown is used for straightening twisted members as wooden framing is completed. If the force P = 30 lb is applied to the handle as shown, determine the normal forces applied to the installed stud at points A and B . Ignore friction. 3/92 A freeway sign measuring 12 ft by 6 ft is supported by the single mast as shown. The sign, supporting framework, and mast together weigh 600 lb, with center of gravity 10 ft away from the vertical centerline of the mast. When the sign is subjected to the direct blast of a 75-mi/hr wind, an average pressure difference of 17.5 lb/ft 2 is developed between the front and back sides of the sign, with the resultant of the wind-pressure forces acting at the center of the sign. Determine the magnitudes of the force and moment reactions at the base of the mast. Such results would be instrumental in the design of the base.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 49/59 3/93 A slender rod of mass m 1 is welded to the horizontal edge of a uniform semicylindrical shell of mass m 2 . Determine an expression for the angle θ with the horizontal made by the diameter of the shell through m 1 . (Consult Table D/3 in Appendix D to locate the center of gravity of the semicircular section.) 3/94 The curved arm BC and attached cables AB and AC support a power line which lies in the vertical y - z plane. The tangents to the power line at the insulator below A make 15° angles with the horizontal y -axis. If the tension in the power line at the insulator is 1.3 kN, calculate the total force supported by the bolt at D on the pole bracket. The weight of the arm BC may be neglected compared with the other forces, and it may be assumed that the bolt at E supports horizontal force only.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 50/59 3/95 The device shown in section can support the load L at various heights by resetting the pawl C in another tooth at the desired height on the fixed vertical column D . Determine the distance b at which the load should be positioned in order for the two rollers A and B to support equal forces. The weight of the device is negligible compared with L .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 51/59 3/96 A large symmetrical drum for drying sand is operated by the geared motor drive shown. If the mass of the sand is 750 kg and an average gear-tooth force of 2.6 kN is supplied by the motor pinion A to the drum gear normal to the contacting surfaces at B , calculate the average offset ¯ 𝑥 of the center of mass G of the sand from the vertical centerline. Neglect all friction in the supporting rollers.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 52/59 3/97 Determine the force P required to begin rolling the uniform cylinder of mass m over the obstruction of height h . 3/98 Each of the three uniform 1200-mm bars has a mass of 20 kg. The bars are welded together into the configuration shown and suspended by three vertical wires. Bars AB and BC lie in the horizontal x - y plane, and the third bar lies in a plane parallel to the x - z plane. Compute the tension in each wire. 3/99 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 .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 53/59 Video Solution: Problem 3/99 3/100 A vertical force P on the foot pedal of the bell crank is required to produce a tension T of 400 N in the vertical control rod. Determine the corresponding bearing reactions at A and B .
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 54/59 3/101 The drum and shaft are welded together and have a mass of 50 kg with mass center at G . The shaft is subjected to a torque (couple) of 120 N · m and the drum is prevented from rotating by the cord wrapped securely around it and attached to point C . Calculate the magnitudes of the forces supported by bearings A and B . Computer-Oriented Problems 3/102 Determine and plot the tension ratio T / mg required to hold the uniform slender bar in equilibrium for any angle θ from just above zero to just under 45°. The bar AB of mass m is uniform. 3/103 Two traffic signals are attached to the 36-ft support cable at equal intervals as shown. Determine the equilibrium configuration angles α , β , and γ , as well as the tension in each cable segment.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 55/59 3/104 In executing the biceps-curl exercise, the man holds his shoulder and upper arm stationary and rotates the lower arm OA through the range 0 ≤ θ ≤ 105°. The detailed drawing shows the effective origin and insertion points for the biceps muscle group. Determine and plot the tension T B in this muscle group over the specified range. State the value of T B for θ = 90°. Neglect the weight of the forearm, and assume slow, steady motion.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 56/59 3/105 The basic features of a small backhoe are shown in the illustration. Member BE (complete with hydraulic cylinder CD and bucket-control links DF and DE ) weighs 1500 lb with mass center at G 1 . The bucket and its load of clay weigh 1000 lb with mass center at G 2 . To disclose the operational design characteristics of the backhoe, determine and plot the force T in the hydraulic cylinder AB as a function of the angular position θ of member BE over the range 0 ≤ θ ≤ 90°. For what value of θ is the force T equal to zero? Member OH is fixed for this exercise; note that its controlling hydraulic cylinder (hidden) extends from near point O to pin I . Similarly, the bucket-control hydraulic cylinder CD is held at a fixed length. 3/106 The mass center of the 1.5-kg link OC is located at G , and the spring of constant k = 25 N/m is unstretched when θ = 0. Plot the tension T required for static equilibrium over the range 0 ≤ θ ≤ 90° and state the values of T for θ = 45° and θ = 90°.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 57/59 3/107 The vertical pole, utility cable, and two guy wires from Prob. 3/83 are shown again here. As part of a design study, the following conditions are considered. The tension T 2 is a constant 1000 N, and its 10° angle is fixed. The 10° angle for T 1 is also fixed, but the magnitude of T 1 is allowed to vary from 0 to 2000 N. For that range of values of T 1 , determine and plot the magnitude of the equal tensions T in cables AD and BE and the angle θ for which the moment at O will be zero. State the values of T and θ for T 1 = 1000 N.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 58/59 3/108 The 125-kg homogeneous rectangular solid is held in the arbitrary position shown by the tension T in the cable. Determine and plot the following quantities as functions of θ over the range 0 ≤ θ ≤ 60°: T , A y , A z , B x , B y , and B z . The hinge at A cannot exert an axial thrust. Assume all hinge force components to be in the positive coordinate directions. Friction at D is negligible.
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12/13/23, 11:27 AM Engineering Mechanics Statics https://education.wiley.com/content/Meriam_Statics_9e/ebook/epub/9781119392620/OPS/c03a.xhtml 59/59
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Subject: Eng. Mech. Dynamics I Tutorial Sheet 5 University of Babylon Kinetics of particles "Work and Energy" Class: 2nd College of Engineering/Al-Musayab Lecturer: Mushrek A. Mahdi 30 Q1: The spring is undeformed (unstretched) when x = 0. If the body moves from the initial position x, = 100 mm to the final position x2 = 200 mm, determine: 2 lb 15 1- The work done by the spring on the body 2- The work done on the body by its weight. [ Ans.: U, = -60 J, Uw = 2.35 J] Q4: The system is released from rest with no slack in the cable and with the spring 4 kN/m www unstretched. Determine the distanced s traveled by the 10-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 2 kg Assume no mechanical interference 7 kg [ Ans.: (a) s = 0. 663 m, (b) s = 0.349 m] 20 10 kg 25 Q2: The 64.4-lb crate slides down the curved path in the vertical plane. If the crate has a velocity of 3 ft/sec down the incline at A and a velocity of 25 ft/sec at B, compute the work U, done on the crate…
CEE 241: Statics University of Nevada, Las Vegas Image copyright © Pearson Education, Inc. Shared with current students using accompanying text by the instructor solely for the purpose of teaching the course and assessing student learning. You should not distribute this document to anyone. The mass of cylinder C is given. Find the mass of cylinder A to maintain equilibrium. Answer: mA = 20 kg D Page 1 / 1 E 130° - C Q+ B 40 kg
Help!!! Answer it correctly!!! Make sure you solve work on hand!!! Answer correctly Please!!!!!!!
ssignment 1 X w Question 15 of 20 - MEC115D As X budy 115D Assignment 1 education.wiley.com/was/ui/v2/assessment-player/index.html?launchid=a980548c-2c92-4eaa-ad4f-5b69df8db94c#/question/14 Question 15 of 20 Answers: Replace the two cable tensions which act on the pulley at O of the beam trolley by two parallel forces which act at pulley connections A and B. The forces are positive if up, negative if down. F₁ = 205 mm 160 mm 205 mm 6.5 KN 4.5 KN B + kN Q Search -/5 = : > 9:09 F 8/21/20
ortal X + kent.ac.uk/2021/pluginfile.php/680076/mod_resource/content/1/EENG3230_2022.pdf 4- Question 3 Two blocks, A and B, of mass m and 3m respectively, are connected through a cable and a pulley (see figure 3.1). Block A is also attached to a spring, which is fixed to the ground and has a spring constant k = 50 N/m. Block B is on an inclined plane forming an angle of 30 degrees with the horizontal line. Block B is released from rest with no slack in the cable and with the spring not being stretched or compressed. Assign to m the value in kg of your body weight, then (a) calculate the distance covered by block B once it stops for the first time; assume that there is no friction. (b) assume a kinetic friction force F = 5 N acts on block B and calculate the distance covered by block B once it stops for the first time. State any assumptions and comment on your solutions. B 3m £ F3 F4 Q DII % F5 ☀ 30° F6 H F7 PrtScn F8 WWW 8 (0 Home F9 W End F10 PgUp F11 PgDn C F12
The pipe assembly is supported by smooth journal bearings at A. B. and C. Suppose that F= 310 N. (Eigure 1) Part A Determine the y and z components of reaction at A using scalar notation Express your answers using three significant figures separated by a comma. V AE I1 vec ? Ay. A, = Submit Request Answer Part B Determine the z and z components of reaction at B using scalar notation. Express your answers using three significant figures separated by a comma. Vo AEd It vec ? Figure В, В, Submit Request Answer • Part C 0.6 m 0.4 m Determine the y and z components of reaction at C using scalar notation. Express your answers using three significant figures separated by a comma. 0.6 m 0.6 m Va AEO| vec ? Cy, C; = N
The structure shown below is used to hold a model of the Millennium Falcon which has a mass of 380 N . W1 W2 h3 E F h2 B h1 A • Member ABCD has the following weight and dimensions: Weight of ABCD = 150 N h1= 0.8 m h2 = 1.8 m h3 = 0.1 m • Member CEF has the following weight and dimensions: Weight of CEF = 200 N w1 = 1.7 m w2 = 0.3 m • The curved member BE is massless. i. Determine the force exerted on the frame from roller D. ii. Determine the magnitude of the x and y components at each of the four pins A, B, C, and D. Part A - Part A Determine the magnitude of the force exerted on member ABCD from roller D. Enter the magnitude of the value in units of N to three significant figures. Templates Symbols Slope/Displacement Vector uado redo reset keyboard shortcuts help Dx = N Submit Request Answer
Statics Problem !!! Help me !!!! Answer it this Problem Correctly!! Please give correct Solution
a 120 Kg car is being lowered slowly unto the dock usig the hoist A and winch C determine the force in cable AV for the positions
MasterngEngineering Masterin , × + Dd Pearson's Mylab & Masteringx eC à https://session masteringengineering.com/myct/itemView?assignmentProblemID-8226923
Need only a handwritten solution only (not a typed one).
97 lll i docs.google.com/forms/d/e, o when you upload files and submit this form. Not adyan.rashid.etcn3@student.atu.edu.iq? Switch account Q/ The mass center G of the 1400-kg rear- engine car is located as shown in the figure. Determine the normal force under each tire when the car is in equilibrium. State any assumptions. 1386 mm - 964 mm Nf= 1500, Nr= 2500 Nf= 2200, Nr= 4050 Nf= 2800, Nr= 4500 None of ablove Nf= 2820, Nr= 4050 Upload the solve
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Don't give Ai solution, I need human expert answer in handwritten format (include FBD) Calculate the tension T (N) required to steadily pull the cable over a roller support on the utility pole. Neglect the effect of the friction. The cable is horizontal at A, has a mass 7kg/m. Also find the length of cable from A to B. Tension "T"(N) A Find the length of cable from A to B (m) 30 m B 10 m
Question 3: The free body diagram of the back model in static equilibrium is shown in Figure 1 below. Develop an equation for T as a function of W in terms of the defined variables. Hint: take a moment about the lower back where Fx and Fy act (i.e. lower lumbar spine). Please show your work! Fx LT LEDER F₁ W₂ Lb W un mun -Lw b Figure 1. Free body diagram of the back model. T is the tension exerted by the extensor muscles (all muscles combined), Wo is the weight of the upper body (torso and arms), W is the weight of the object held in the hand. LT is the perpendicular moment arm of T; Lo and Lw are the perpendicular moment arms of W, and W. A
Panopto Document Sharing Access Pearson User Settings Purchase Options The 22-kg flowerpot is supported at A by the three cords as shown in (Figure 1). Figure D 60° 3077 300 45° B 1 of 1 mylabmastering.pearson.com P Pearson MyLab and Mastering Part A P Course Home b Success Confirmation of Question Submissi... Determine the force acting in cord AB for equilibrium. Express your answer to three significant figures and include the appropriate units. ☐ μÅ FAB = Value Units Submit Request Answer Part B ? Determine the force acting in cord AC for equilibrium. Express your answer to three significant figures and include the appropriate units. Α FAC = Value Units Submit Request Answer ་ Part C ? Determine the force acting in cord AD for equilibrium. Express your answer to three significant figures and include the appropriate units. μÅ ? FAD = Value Units
2. Find the horizontal force P to start the motion of any part of the system of three blocks resting upon one another as shown. The weight of the blocks are W-300 KN, Ws= 100 KN and Wc =200 KN. Between A and B μ=0.30, between C and B, μ =0.20 and between C and the ground, p=0.10. 1 sni brod nog 02.0-4 B C 05.0-4 Solution: tamos quoy worla bre sosia asquar 005 300 en of jells400 N₁-300 F3 N-300- N₂=300 Assuming B and C will not move. F₁ = 300 (0.30) F₁ = 90 kN ne à bns A zelboß 1 P = 90 kN es ensla berb hebnu 02.0- y elin 05.0= q V in Celpris orllanimetsa MX 008 Assuming C will not move: al 1st F2=400 (0.20) = 80 kN OTE Bm ribirte F₂ vica Assuming the three blocks move: F3 = 0.10 (600) F3 = 60 kN P=60 KN Least force is 60 kN.
Determine the equivalent spring constant of the system where the spring will be located in the position of k1. k1=1N/m, k2=5N/m (answer in N/m) * Sphere, mass m, No slip Bell crank lever, - mass moment of inertia Jo 06. m
A 10 g hanger is placed on a device as shown. The pegs are evenly spaced and label 1 through 13. Hangers of various masses are available. (Taking 1 equally space=10 cm) 8 9 10 " 2 3 4 12 13 a) What mass will balance the 10g hanger when placed on peg no 1? b) Where should you put a 15g hanger to balance the 10g hanger? (The unknown hanger is removed)
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