Vector Mechanics for Engineers: Statics and Dynamics
12th Edition
ISBN: 9781259638091
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 3.4, Problem 3.126P
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A farmer uses cables and winch pullers B and E to plumb one side of a small barn. If it is known that the sum of the moments about the X axis of the forces exerted by the cables on the barn at points A and D is equal to 4728 lb·ft, determine the magnitude of TDE when TAB = 255 lb.
A blade held in a brace is used to tighten a screw at A. (a) Determine the forces exerted at B and C, knowing that these forces are equivalent to a force-couple system at A consisting of R = −(25 N)i + Ry j + Rzk and MA R = −(13.5 N·m)i. (b) Find the corresponding values of Ry and Rz. (c) What is the orientation of the slot in the head of the screw for which the blade is least likely to slip when the brace is in the position shown?
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Chapter 3 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 3.1 - A foot valve for a pneumatic system is hinged at...Ch. 3.1 - 3.2A foot valve for a pneumatic system is hinged...Ch. 3.1 - It is known that a vertical force of 200 lb is...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - An 8-lb force P is applied to a shift lever....Ch. 3.1 - For the shift lever shown, determine the magnitude...Ch. 3.1 - An 11-lb force P is applied to a shift lever. The...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...
Ch. 3.1 - 3.11 and 3.12The tailgate of a car is supported by...Ch. 3.1 - 3.11 and 3.12The tailgate of a car is supported by...Ch. 3.1 - 3.13 and 3.14It is known that the connecting rod...Ch. 3.1 - 3.13 and 3.14It is known that the connecting rod...Ch. 3.1 - Form the vector product P1 P2 and use the result...Ch. 3.1 - The vectors P and Q are two adjacent sides of a...Ch. 3.1 - A plane contains the vectors A and B. Determine...Ch. 3.1 - A line passes through the points (4 m, 3 m) and (2...Ch. 3.1 - Prob. 3.19PCh. 3.1 - Determine the moment about the origin O of the...Ch. 3.1 - Before the trunk of a large tree is felled, cables...Ch. 3.1 - The 12-ft boom AB has a fixed end A. A steel cable...Ch. 3.1 - A 200-N force is applied as shown to the bracket...Ch. 3.1 - A force P of magnitude 200 N acts along the...Ch. 3.1 - A 6-ft-long fishing rod AB is securely anchored in...Ch. 3.1 - A precast concrete wall section is temporarily...Ch. 3.1 - In Prob. 3.22, determine the perpendicular...Ch. 3.1 - In Prob. 3.23, determine the perpendicular...Ch. 3.1 - In Prob. 3.24, determine the perpendicular...Ch. 3.1 - In Prob. 3.25, determine the perpendicular...Ch. 3.1 - In Prob. 3.25, determine the perpendicular...Ch. 3.1 - In Prob. 3.26, determine the perpendicular...Ch. 3.1 - In Prob. 3.26, determine the perpendicular...Ch. 3.1 - Determine the value of a that minimizes the...Ch. 3.2 - Given the vectors P = 2i + j + 2k, Q = 3i + 4j ...Ch. 3.2 - Form the scalar product B C and use the result...Ch. 3.2 - Three cables are attached to the top of the tower...Ch. 3.2 - Three cables are attached to the top of the tower...Ch. 3.2 - Knowing that the tension in cable AC is 280 lb,...Ch. 3.2 - Prob. 3.40PCh. 3.2 - Ropes AB and BC are two of the ropes used to...Ch. 3.2 - Prob. 3.42PCh. 3.2 - The 20-in. tube AB can slide along a horizontal...Ch. 3.2 - Solve Prob. 3.43 for the position corresponding to...Ch. 3.2 - Determine the volume of the parallelepiped of Fig....Ch. 3.2 - Given the vectors P = 3i + 2j + k, Q = 5i + j 2k,...Ch. 3.2 - A crane is oriented so that the end of the 25-m...Ch. 3.2 - 3.48The 25-m crane boom AO lies in the yz plane....Ch. 3.2 - To loosen a frozen valve, a force F with a...Ch. 3.2 - 3.50When a force F is applied to the handle of the...Ch. 3.2 - The 0.61 1.00-m lid ABCD of a storage bin is...Ch. 3.2 - 3.52The 0.61 1.00-m lid ABCD of a storage bin is...Ch. 3.2 - A farmer uses cables and winch pullers B and E to...Ch. 3.2 - Solve Prob. 3.53 when the tension in cable AB is...Ch. 3.2 - A force P of magnitude 520 lb acts on the frame...Ch. 3.2 - 3.56A force P acts on the frame shown at point E....Ch. 3.2 - The frame ACD is hinged at A and D and is...Ch. 3.2 - In Prob. 3.57, determine the moment about the...Ch. 3.2 - The triangular plate ABC is supported by...Ch. 3.2 - 3.60The triangular plate ABC is supported by...Ch. 3.2 - A regular tetrahedron has six edges of length a. A...Ch. 3.2 - Prob. 3.62PCh. 3.2 - Prob. 3.63PCh. 3.2 - In Prob. 3.55, determine the perpendicular...Ch. 3.2 - In Prob. 3.56, determine the perpendicular...Ch. 3.2 - In Prob. 3.57, determine the perpendicular...Ch. 3.2 - In Prob. 3.58, determine the perpendicular...Ch. 3.2 - In Prob. 3.59, determine the perpendicular...Ch. 3.2 - In Prob. 3.60, determine the perpendicular...Ch. 3.3 - Two 80-N forces are applied as shown to the...Ch. 3.3 - Two parallel 60-N forces are applied as shown to...Ch. 3.3 - A multiple-drilling machine is used to drill...Ch. 3.3 - Four pegs of the same diameter are attached to a...Ch. 3.3 - Prob. 3.74PCh. 3.3 - The shafts of an angle drive are acted upon by the...Ch. 3.3 - If P = 0 in the figure, replace the two remaining...Ch. 3.3 - 3.77If P = 20 lb in the figure, replace the three...Ch. 3.3 - The two couples shown are to be replaced with a...Ch. 3.3 - Solve part a of Prob. 3.78, assuming that two 15-N...Ch. 3.3 - Shafts A and B connect the gear box to the wheel...Ch. 3.3 - A 500-N force is applied to a bent plate as shown....Ch. 3.3 - Prob. 3.82PCh. 3.3 - Prob. 3.83PCh. 3.3 - A 30-lb vertical force P is applied at A to the...Ch. 3.3 - A worker tries to move a rock by applying a 360-N...Ch. 3.3 - A worker tries to move a rock by applying a 360-N...Ch. 3.3 - The shearing forces exerted on the cross section...Ch. 3.3 - Knowing that = 60, replace the force and couple...Ch. 3.3 - Three control rods attached to a lever ABC exert...Ch. 3.3 - A rectangular plate is acted upon by the force and...Ch. 3.3 - While tapping a hole, a machinist applies the...Ch. 3.3 - Prob. 3.92PCh. 3.3 - Replace the 250-kN force P with an equivalent...Ch. 3.3 - A 2.6-kip force is applied at point D of the...Ch. 3.3 - Prob. 3.95PCh. 3.3 - To keep a door closed, a wooden stick is wedged...Ch. 3.3 - A 46-lb force F and a 2120-lbin. couple M are...Ch. 3.3 - Prob. 3.98PCh. 3.3 - Prob. 3.99PCh. 3.3 - Prob. 3.100PCh. 3.4 - 3.101A 4-m-long beam is subjected to a variety of...Ch. 3.4 - A 4-m-long beam is loaded as shown. Determine the...Ch. 3.4 - Determine the single equivalent force and the...Ch. 3.4 - Five separate force-couple systems act at the...Ch. 3.4 - The weights of two children sitting at ends A and...Ch. 3.4 - Three stage lights are mounted on a pipe as shown....Ch. 3.4 - A beam supports three loads of given magnitude and...Ch. 3.4 - A 6 12-in. plate is subjected to four loads as...Ch. 3.4 - Gear C is rigidly attached to arm AB. If the...Ch. 3.4 - To test the strength of a 625 500-mm suitcase,...Ch. 3.4 - Prob. 3.111PCh. 3.4 - Prob. 3.112PCh. 3.4 - The roof of a building frame is subjected to the...Ch. 3.4 - Prob. 3.114PCh. 3.4 - A couple M and the three forces shown are applied...Ch. 3.4 - A machine component is subjected to the forces and...Ch. 3.4 - Prob. 3.117PCh. 3.4 - As follower AB rolls along the surface of member...Ch. 3.4 - A machine component is subjected to the forces...Ch. 3.4 - Two 150-mm-diameter pulleys are mounted on line...Ch. 3.4 - As an adjustable brace BC is used to bring a wall...Ch. 3.4 - In order to unscrew the tapped faucet A, a plumber...Ch. 3.4 - Prob. 3.123PCh. 3.4 - Four forces are applied to the machine component...Ch. 3.4 - A blade held in a brace is used to tighten a screw...Ch. 3.4 - A mechanic uses a crowfoot wrench to loosen a bolt...Ch. 3.4 - Four horizontal forces act on a vertical...Ch. 3.4 - Determine the magnitude of the force P for which...Ch. 3.4 - Prob. 3.129PCh. 3.4 - Prob. 3.130PCh. 3.4 - A concrete foundation mat of 5-m radius supports...Ch. 3.4 - Prob. 3.132PCh. 3.4 - Three forces of the same magnitude P act on a cube...Ch. 3.4 - A piece of sheet metal is bent into the shape...Ch. 3.4 - Prob. 3.135PCh. 3.4 - Prob. 3.136PCh. 3.4 - Two bolts at A and B are tightened by applying the...Ch. 3.4 - Two bolts at A and B are tightened by applying the...Ch. 3.4 - Prob. 3.139PCh. 3.4 - Prob. 3.140PCh. 3.4 - Prob. 3.141PCh. 3.4 - Prob. 3.142PCh. 3.4 - Replace the wrench shown with an equivalent system...Ch. 3.4 - Prob. 3.144PCh. 3.4 - Show that a wrench can be replaced with two...Ch. 3.4 - Show that a wrench can be replaced with two...Ch. 3 - A 300-N force P is applied at point A of the bell...Ch. 3 - A winch puller AB is used to straighten a fence...Ch. 3 - A small boat hangs from two davits, one of which...Ch. 3 - Prob. 3.150RPCh. 3 - A single force P acts at C in a direction...Ch. 3 - The 23-in. vertical rod CD is welded to the...Ch. 3 - In a manufacturing operation, three holes are...Ch. 3 - A 260-lb force is applied at A to the rolled-steel...Ch. 3 - The force and couple shown are to be replaced by...Ch. 3 - Prob. 3.156RPCh. 3 - Prob. 3.157RPCh. 3 - While using a pencil sharpener, a student applies...
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- For the cables of Prob. 2.46, it is known that the maximum allowable tension is 600 N in cable AC and 750 N in cable BC . Determine (a) the maximum force P that can be applied at C, (b) the corresponding value of a.(Reference to Problem 2.46):Two cables are tied together at C and are loaded as shown. Knowing that P = 500 N and a = 60°, determine the tension in (a) in cable AC, (b) in cable BC.arrow_forwardA blade held in a brace is used to tighten a screw at A. (a) Determinethe forces exerted at B and C, knowing that these forces are equivalent to a force-couple system at A consisting of R =-(30 N)i + Ry j+ Rz k and M = –(12 N · m)i. (b) Find the corresponding values of Ry and Rz. (c) What is the orientation of the slot in the head of the screw for which the blade is least likely to slip when the brace is in the position shown?arrow_forwardA machine component is subjected to the forces and couples shown. The component is to be held in place by a single rivet that can resist a force but not a couple. For P = 0, determine the location of the rivet hole if it is to be located (a) on line FG , (b) on line GH.arrow_forward
- In order to unscrew the tapped faucet A , a plumber uses two pipe wrenches as shown. By exerting a 40-lb force on each wrench at a distance of 10 in. from the axis of the pipe and in a direction perpendicular to the pipe and to the wrench, he prevents the pipe from rotating, and thus he avoids loosening or further tightening the joint between the pipe and the tapped elbow C . Determine (a) the angle 0 that the wrench at A should form with the vertical if elbow C is not to rotate about the vertical, (b) the force-couple system at C equivalent to the two 40-lb forces when this condition is satisfied.arrow_forwardSlider P can move along rod OA. An elastic cord PC is attached to the slider and to the vertical member BC. Knowing that the distance from O to P is 6 in. and that the tension in the cord is 3 lb, determine (a) the angle between the elastic cord and the rod OA, (b) the projection on OA of the force exerted by cord PC at point P.arrow_forwardKnowing that the tension in cable AC is 2130 N, determine the components of the force exerted on the plate at C.arrow_forward
- In order to unscrew the tapped faucet A, a plumber uses two pipe wrenches as shown. By exerting a 40-lb force on each wrench, at a distance of 10 in. from the axis of the pipe and in a direction perpendicular to the pipe and to the wrench, he prevents the pipe from rotating, and thus avoids loosening or further tightening the joint between the pipe and the tapped elbow C. Determine (a) the angle θ that the wrench at A should form with the vertical if elbow C is not to rotate about the vertical, (b) the force-couple system at Cequivalent to the two 40-lb forces when this condition is satisfied.arrow_forwardA machine component is subjected to the forces and couples shown.The component is to be held in place by a single rivet that can resista force but not a couple. For P=0, determine the location of the rivet hole if it is to be located (a) on line FG, (b) on line GH.arrow_forwardA machine component is subjected to the forces and couples shown. The component is to be held in place by a single rivet that can resist a force but not a couple. ForP= 60 N, determine the location of the rivet hole ifit is to be located (a) from G on line FG, (b) from G on line GH.arrow_forward
- Cable AC exerts on beam AB a force P directed along line AC . Knowing that P must have a 350-lb vertical component, determine (a) the magnitude of the force P, (b) its horizontal component.arrow_forwardA mechanic uses a crowfoot wrench to loosen a bolt at C . The mechanic holds the socket wrench handle at points A and B and applies forces at these points. Knowing that these forces are equivalent to a force-couple system at C consisting of the force C = -(8 lb)i + (4 lb) k and the couple MC= (360 lb·in.)i, determine the forces applied at A and at B when Az = 2 ib.arrow_forward(a) Show that, when a frame supports a pulley at A , an equivalent loading of the frame and of each of its component parts can be obtained by removing the pulley and applying at A two forces equal and parallel to the forces that the cable exerted on the pulley. (b) Show that, if one end of the cable is attached to the frame at a point B , a force of magnitude equal to the tension in the cable should also be applied at B.arrow_forward
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