in the class. In addition, selected problems with solutions have been included to Free body diagram (FBD) is the most important first step in the mechanics. Problems & Solutions In Engineering Mechanics book. Read 7 reviews from the world's largest community for readers. Each chapter begins with a quick discu. Solving Practical Engineering Mechanics Problems: Statics. Sayavur I. A solution of one similar sample problem from each topic is provided. This first book .
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ENGINEERING MECHANICS-Solution Equilibrium Prob - Free download as Word Doc .doc /.docx), PDF File .pdf), Text File .txt) or read online for free. PROBLEM A cylinder weighing lb is held against a smooth incline. Engineers are keen to use the laws of mechanics to actual field problems. Application of laws of mechanics to field problem is termed as Engineering Mechanics. Engineering mechanics friction problems B A m SOLUTION m m Equations of Equilibrium: The normal reactions acting on the wheels .
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ENGINEERING MECHANICS-Solution Equilibrium Prob 308-361
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Preferred contact method Email Text message. When will my order be ready to collect? The car has a mass of 1. If the coefficient of static friction between the shoulder of the road 2. Also, if the man has a weight of lb, determine the smallest coefficient of static friction between his shoes and the floor so that he does not slip. Fm - Nm The 5-kg cylinder is suspended from two equal-length cords. Referring to the FBD shown in Fig. Using the result of I, The 5-kg cylinder is suspended from two equal-length d cords.
The end of each cord is attached to a ring of negligible mass, which passes along a horizontal shaft. When the ring is on the verge to sliding along the rod, slipping will have to occur. The board can be adjusted vertically by tilting it up and F sliding the smooth pin A along the vertical guide G. When 6 in. Determine the largest dimension d which will support any applied force F without G A Top view causing the board to slip downward.
C Side view 0. The uniform pole has a weight W and length L. Its end B is tied to a supporting cord, and end A is placed against the C wall, for which the coefficient of static friction is ms. Determine the largest angle u at which the pole can be placed without slipping. The boards could be on the verge of slipping between the two boards at the ends or between the clamp. Let n be the number of boards between the clamp. Thus, the number of boards between the two boards at the ends is n - 2.
Referring to the free-body diagram shown in Fig. By b ed e n in no W iss ea s itt id tio is e D t w t p or em ch referring to the free-body diagram shown in Fig. P Determine the maximum vertical force P that may be mm mm applied to link AB without causing the disk to slip at C. If the disk is on the verge of moving, slipping would have to occur at.
We or point C. Substituting this value into Eqs. Determine where he should position his center of gravity G at d in order to exert the maximum horizontal force on the door.
What is this force? Referring to the FBD of the crate shown in Fig. Thus the frictional force developed is. Thus, the frictional force t p or em ch d th g.
If the crate is on the verge of moving, slipping will have to occur. The man has a weight of lb and a center of gravity at G. Thus, the frictional forces FA and FC must act upward as indicated on the free-body diagram of the man shown in Fig. We or: The friction pawl is pinned at A and rests against the wheel at B.
It allows freedom of movement when the wheel is A rotating counterclockwise about C. Clockwise rotation is prevented due to friction of the pawl which tends to bind the wheel.
Neglect the weight of the pawl so that it becomes a two-force member. When the wheel is on the verge of rotating, slipping would have to occur. Neglect the mass of the rods. Due to the symmetrical loading and system, ends A and B of A B the rod will slip simultaneously. Since end B tends to move to the right, the friction force FB must act to the left as indicated on the free-body diagram shown in Fig.
Due to the symmetrical loading and system, ends A and B of the rod will slip simultaneously. Determine if the semicylinder slides down the plane, and if not, find the angle of tip u of its base AB. The semicylinder of mass m and radius r lies on the rough B inclined plane.
If the semicylinder is on the verge of moving, slipping would have to occur. Determine if the man can move the crate.
Since P tends to move the crate to the right, the frictional force FC will act to the left as indicated on the free - body diagram shown in Fig. Since the crate is required to be on the verge of sliding the magnitude of FC can be computed using the friction formula, i. As indicated on the free - body diagram of the man shown in Fig. Thus, de f a rse de ot he can move the crate. Since force P tends to move the crate to the right, the frictional force FC will act to the left as indicated on the free - body diagram shown in Fig.
The thin rod has a weight W and rests against the floor and wall for which the coefficients of static friction are mA and mB, respectively. Determine the smallest value of u for B which the rod will not move.
If the rod is on the verge of moving, slipping will have to occur at points A and B. Substituting these values into Eqs.
The lb boy stands on the beam and pulls on the cord with a force large enough to just cause him to slip. The D A B beam is uniform and has a weight of lb.
Neglect the size C of the pulleys and the thickness of the beam. The lb boy stands on the beam and pulls with a force of 40 lb. The 5 12 beam is uniform and has a weight of lb. Neglect the size D A B of the pulleys and the thickness of the beam. Therefore, the friction force developed is.
Problems & Solutions In Engineering Mechanics
Determine the smallest force the man must exert on the rope in order to move the kg crate. Also, what is the angle u at this moment? Two blocks A and B have a weight of 10 lb and 6 lb, respectively.
Determine the incline angle u for which both blocks begin A to slide. Also find the required stretch or compression in the connecting spring for this to occur.
If block A and B are on the verge to move, slipping would have to occur an on in rs h at point A and B. Determine the angle u which will cause motion of one of A the blocks.
What is the friction force under each of the blocks when this occurs? The friction hook is made from a fixed frame which is shown colored and a cylinder of negligible weight. A piece of paper is placed between the smooth wall and the cylinder. The uniform rod has a mass of 10 kg and rests on the inside of the smooth ring at B and on the ground at A. If the rod is on the verge of slipping, determine the coefficient of static C friction between the rod and the ground.
The rings A and C each weigh W and rest on the rod, which d has a coefficient of static friction of ms. If the suspended ring at B has a weight of 2W, determine the largest distance d A C between A and C so that no motion occurs. Neglect the weight of the wire. The wire is smooth and has a total length of l. The tension developed in the wire can be obtained by considering the equilibrium of the free-body diagram shown in Fig.
Here, the equilibrium of ring C will be considered. Since ring C is required to be on the verge of sliding to. Using the result of T and referring to Fig. It is supported at one end by a pin and at the other end by a post having a A B mass of 50 kg and negligible thickness.
Determine the P minimum force P needed to move the post. NC - NB The beam AB has a negligible mass and thickness and is N subjected to a force of N. It is supported at one end by a pin and at the other end by a spool having a mass of 40 kg. Therefore the above assumption is correct. If each box weighs lb, determine the least horizontal 3 ft force P that the man must exert on the top box in order to cause motion.
There are three possible motions, namely 1 the top box slides, 2 both boxes slide together as a single unit on the ground, and 3 both boxes tip as a single unit about point B. Using the result of P and te is ss th ite considering the equilibrium of the free - body diagram shown in Fig. Thus, the w le co ro is above assumption is correct. We will assume that both boxes tip as a A B single unit about point B. Using the result of P and considering the equilibrium of the free - te is ss th ite body diagram shown in Fig.
The block of weight W is being pulled up the inclined P plane of slope a using a force P. Determine the angle f at which P should act on the block P so that the magnitude of P is as small as possible to begin f pushing the block up the incline. What is the corresponding value of P? The block weighs W and the slope a is known. A cord wrapped around it is attached to the top 1. The uniform beam has a weight W and length 4a. It rests on the fixed rails at A and B. If the coefficient of static friction 3a at the rails is ms, determine the horizontal force P, applied a perpendicular to the face of the beam, which will cause the beam to move.
The beam will slip at A first. Determine the greatest angle u so that the ladder does not slip when it supports the kg man in the position shown.
C The surface is rather slippery, where the coefficient of static 0. The slipping could occur at either end A or B of the ladder. We will assume that slipping occurs at end B.
A B Equations of Equilibrium: Thus, an his e the above assumption is correct. The uniform 6-kg slender rod rests on the top center of the C 3-kg block.
Therefore, the above assumption is correct. The disk has a weight W and lies on a plane which has a z coefficient of static friction m. Determine the maximum height h to which the plane can be lifted without causing the disk to slip. The unit vector perpendicular to the inclined plane can be determined using cross product. Determine the largest angle u that will cause the wedge to be self-locking regardless of the magnitude of horizontal P P u force P applied to the blocks.
Neglect the weight of the wedge. For the wedge to be self-locking, the frictional force F indicated on the free-body diagram of the wedge shown in Fig.
Neglect the weight and size of the B wedge and the thickness of the beam. If the wedge is on the verge of moving to the right, then slipping will have to occur at both contact surfaces. The stub is free to move without friction within the fixed collar C. Neglect the C weights of the slider and stub. Neglect the weight of A and B. Referring to the FBD of the cylinder, Fig. Determine the minimum applied force P required to move wedge A to the right.
The spring is compressed a distance of mm. Determine the largest weight of the wedge that can be placed between the 8-lb cylinder and the wall without upsetting equilibrium. We or FA If the spring is compressed mm 15 when in the position shown, determine the smallest force P A B needed to move wedge C to the left.
Neglect the weight of 15 C P the wedges. NAB - 0. Neglect the weight of the wedges. The single square-threaded screw of the A B clamp has a mean diameter of 1 in. We or Note: Since fs 7 u, the screw is self-locking. If the clamping force on the boards is lb, determine the 6 in. The single square-threaded screw has a mean diameter of 1 in. The column is used to support the upper floor. If the force F is removed from the handle of the jack in Prob. If the clamping force at G is N, determine the horizontal mm mm force F that must be applied perpendicular to the handle of G C the lever at E.
The mean diameter and lead of both single A square-threaded screws at C and D are 25 mm and 5 mm, respectively.
The mean diameter and lead of the single A square-threaded screw at C and D are 25 mm and 5 mm, respectively. Since fs 7 u, the screws are self-locking. A turnbuckle, similar to that shown in Fig. The screws have a mean radius of 6 mm and a lead of 3 mm. Applying Eq.
It will not unscrew even if moment M in no W iss ea s itt id tio is e D t w t p or em ch is removed. Joint C: Determine the torque M which must be applied to the turnbuckle to draw the screws closer together, so that the compressive force of N is 4m developed in member BC. C A Joint B: Since friction at two screws must be -1 It will not unscrew even if moment M te is ss th ite is removed. The shaft has a square-threaded screw with a lead of 8 mm 15 mm and a mean radius of 15 mm.
If it is in contact with a plate gear having a mean radius of 30 mm, determine the resisting torque M on the plate gear which can be overcome if a B torque of 7 N m is applied to the shaft. Neglect friction of the bearings located at A and B. It will not unscrew even if force F is m W ina g b ed e n in no W iss ea s itt id tio removed.
The square-threaded screw has a mean diameter of 20 mm and a lead of 4 mm. If the weight of the plate A is 5 lb, determine the smallest coefficient of static friction between the screw and the plate so that the plate does not travel down the screw when the plate is suspended as shown.
Since fS 7 u, the screw is self-locking. It will not unscrew even if moment M of rk stu e o tat ity o g us d S is removed. Thus when turned, the screw draws the two arms together. It will not unscrew even if moment M d th g.
Determine the horizontal force P that must be applied A perpendicular to the handle of the lever at A in order to develop a compressive force of 12 kN on the material. T - A cylinder having a mass of kg is to be supported by the cord which wraps over the pipe.
F Applying Eq. Determine the largest vertical force F that can be applied to the cord without moving the cylinder.
If the tension in the rope, caused by the ship, is lb, determine the least number of complete turns the rope must be wrapped around the capstan in order lb to prevent slipping of the rope. The greatest horizontal force that a longshoreman can exert on the rope is 50 lb. Thus 2p. Determine the required force P to begin lifting the cylinder.
The rope passes over a rough peg with two and half turns.Determine if the semicylinder slides down the plane, and if not, find the angle of tip u of its base AB. The pulleys form two sprockets for an endless chain looped over them in two loops. The floor-polishing machine rotates at a constant angular velocity. Such a body cannot exist theoretically. Popular in Angle. The shaft itself cannot rotate. Problem The cantilever beam shown in Fig.
Sahithi Mukkavilli rated it it was amazing Nov 18, P is supported at D and a roller at C which separates the upper and lower beams. If you have changed your email address then contact us and we will update your details.
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