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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Textbook Question
Chapter 3.1, Problem 3.16P
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The magnitude of two vectors A and B shown in the figure below are respectively A =
3m and B 1.5 m. The magnitude(R) and the direction (6) of their resultant R = A+
B are equal to:
R= 1.239 m e = 43.29 degree
R = 1.859 m ; 0 23.79 degree
R = 1.239 m; 6e 23.79 degree
R = 1.859 m;e = 43.29 degree
R = 0.620 m;e = 23.79 degree
Express the 40 lb force in the rope from point A to point C in cartesian format. Point C is in the x-y plane
and at an angle of 20 degrees from the y axis as shown.
4 ft
20 lb
A
B
3 ft
X
40 lb
Z
2 ft
1.5 ft
4.87i+27.6j - 28.5k lb
-4.87i+27.6j + 28.5k lb
-4.87i+27.6j - 28.5k lb
4.87i+22.8j - 32.5k lb
2 ft
20
y
C
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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- F1 F2 F3 A F4 D Consider the following values: - F5 a - 13 m; b - 3 m; G - 13 m; d - 3 m; F1 = 3 kN; F2 = 11 kN; F3 = 2 kN; F4 = 20 kN; F5 = 2 kN; a = 30°, 0= 60°, B = 30° 1] What is the resultant moment of the five forces acting on the rod about point A? a) - 15.8 kN.m b) 55.7 kN.m e) 141.6 kN.m d) 17.9 kN.m e) 49.1 kN.m ) 31.3 kN.marrow_forward2000Lbs 30° 60° y A' \ B The bar OA is fully constrained at O and attached to the cable AB. The bar length is 20', and it forms a 30° angle with the z-axis and its projection on the x– y plane forms a 60° angle with the x-axis. The point B is prescribed by the coordinates (8',16',0). If the force in the cable is 2000Lbs, what is the moment of this force about O? What is the moment of the 2000Lbs force about the axis OÁ.arrow_forwardF1 F2 ba C F3 A B d. b F4 Consider the following values: - F5 a = 7 m; b = 3 m; c = 7 m; d = 3 m; F1 = 3 kN; F2 = 11 kN; F3 = 2 kN; F4 = 20 kN; F5 = 2 kN; a = 30° e = 60° , B = 30° 1] What is the resultant moment of the five forces acting on the rod about point A? a) 90.8 kN.m b) 72.7 kN.m c) 14.6 kN.m d) 55.9 kN.m e) 21.6 kN.m f) 61.3 kN.m 2] What is the resultant moment of the five forces acting on the rod about point B? a) 77.8 kN.m b) 25.7 kN.m c) 38.6 kN.m d) 18.9 kN.m e) 37.9 kN.m f) 84.2 kN.m 3] What is the resultant moment of the five forces acting on the rod about point C? a) 35.7 kN.m b) 21.1 kN.m c) 714.6 kN.m d) 69.1 kN.m e) 51.4 kN.m f) 85.3 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) 17.8 kN.m b) 55.7 kN.m c) 44.6 kN.m d) 18.9 kN.m e) 21.5 kN.m f) 30.1 kN.m 5] What is the moment of the force F2 about point E? a) 81.7 kN.m b) 78.1 kN.m c) 64.6 kN.m d) 73.1 kN.m e) 54.6 kN.m f) 61.3 kN.marrow_forward
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- Add the following forces to find the resultant force. V1 = 150 g @ 470 V2 = 550 @ 324° V3 = 350 g @ 215° V4 = 250 @ 172° V5 = 450 g @ 285°arrow_forwardSolve Q2arrow_forwardN m A 150 N 300 mm 250 mm P N 400 mm 90 N Question Determine the magnitude of the resultant force (in N) of the coplanar force system shown in the figure below where the horizontal force P = 248 N and the couple M = 568 Nm. Determine the angle (in degrees) that the resultant makes with the positive x-axis, which is in the same direction as the horizontal force P. If the resultant force calculated in Q8 is placed at A, determine the magnitude of the couple created in Nm. Determine the distance from A (in m) at which this resultant should be placed so that the system is replaced entirely by a single force. If the resultant force calculated in Q8 is placed at O, determine the magnitude of the couple created in Nm. Determine the distance from O (in m) at which this resultant should be placed so that the system is replaced entirely by a single force.arrow_forward
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