VECTOR MECHANICS FOR ENGINEERS W/CON >B
12th Edition
ISBN: 9781260804638
Author: BEER
Publisher: MCG
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Textbook Question
Chapter 3.2, Problem 3.45P
Determine the volume of the parallelepiped of Fig. 3.20b when
(a) P = 2i – 4j + 3k, Q = –5i – j + 2k, and S = i – 7j – k
(b) P = 6i – 5j – 2k, Q = i + 2j + 3k, and S = – 4i – 3j + 2k
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Students have asked these similar questions
Compare the magnitudes of the equilibrant vectors measured from the experiment with
those obtained from the graphical and component methods.
Example: A: 200 g 60° above +x axis
B: 300 g 45° above -x axis
C: 400 g 30°below -x-axis
A, A cos a = 1.96 N x cos 60° = 0.98 N
B₂B cos b = 2.94 N x cos 135º = -2.08 N
C, C cos g = 3.92 N x cos 210°= -3.39 N
R₂-A, + B + C₂ = -4.49 N
A, A sin a = 1.96 N x sin 60° = 1.70 N
By
B sin b = 2.94 N x sin 135º = 2.08 N
C, C sin g = 3.92 N x sin 210° = -1.96 N
Ry= Ay+ By + Cy = 1.82 N
Questions:
I: (a) A: 200 g along +x axis
B: 100 g 45° above -x axis
A₂ = A cos a =
B₂ =B cos b =
R₂-A₂+ B₁₂=
A₂ = A sin a =
B, = B sin b =
R₂ = A + B₂ =
R=(R₂. R₂):_ Quadrant
R = √ (R₂²+R₂²) =
Direction:q=tan [R, /R.]
(c)
A: 100 g along -y axis
B: 200 g along -x axis
A = A cos a =
B = B cos b =
R₂-A₂+ B₂ =
A = A sin a =
B, B sin b =
R=A, +B₂ =
R=(R₁, R₂): Quadrant
R = √ (R₂²+R₂²) =
Direction:q tan¹ [R, /R]
Example ( 2-1) :
The ring in the figure below is subjected to two forces ( F1) and ( F2).
Determine the magnitude and direction of the resultant force.
10°
F, = 150 N
F = 100 N
%3D
15°
Solution :
Parallelogram Law. The parallelogram is formed by drawing a line from the head of F1 that
is parallel to F2 , and another line from the head of F2 that is parallel to F1 , the resultant
force FR extends to where these lines intersect at point A. The two unknowns are the
magnitude of ( FR) and the angle ( 0) (theta).
Q4/ For the figure below, all
dimensions in inch. A/The total Area :
3
1.5
2.5
2.5
2.5
2.5
Q4/B/ the value of X-bar is:
Q4/C/ The value of Y-bar is:
Chapter 3 Solutions
VECTOR MECHANICS FOR ENGINEERS W/CON >B
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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- GO 321 3 in F1 F2 a F3 A d F4 F5 Consider the following values: - a = 25 m; b = 5 m; c = 25 m; d = 5 m; F1 = 7 kN; F2 = 8 kN; F3 = 9 kN; F4 = 10 kN; F5 = 11 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) - 158 kN.m b) 127 kN.m c) 146 kN.m d) - 103 kN.m e) 241 kN.m f) - 171 kN.m 2] What is the resultant moment of the five forces acting on the rod about point B? a) 98.8 kN.m b) - 291.7 kN.m c) 311.6 kN.m d) – 264.6 kN.m e) 354.2 kN.m f) - 242.5 kN.m 3] What is the resultant moment of the five forces acting on the rod about point C? a) 86.7 kN.m b) - 141.1 kN.m c) 14.6 kN.m d) - 272.1 kN.m e) 174.1 kN.m f) - 315.3 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) - 117.8 kN.m b) 82.7 kN.m c) 121.9 kN.m d) - 259.9 kN.m e) 127.1 kN.m f) 300.1 kN.m Activate 5] What is the moment of the force F2 about point E? a) 151.7 kN.m b) 118.1 kN.m c) 214.6 kN.m d) 158.6 kN.m e) 101.1 kN.m loarrow_forwardA square plate with sides 1.5 m in length can rotate around an axle passing through its center of mass (CM) and perpendicular to its surface (see figure below). There are four forces acting on the plate at different points. The rotational inertia of the plate is 16 kg - m². Use the values given in the figure to answer the following questions. (Assume 0 = 40°. Express your answers in vector form.) 30.0 N 60.0 N CM 20.0 N 40.0 N (a) What is the net torque acting on the plate?arrow_forwardF1 F2 F3 A B d b F4 D F5 Consider the following values: - a = 25 m; b = 5 m; c = 25 m; d = 5 m; F1 - 6 kN; F2 - 7 kN; F3 = 8 kN; F4 - 9 kN; F5 - 10 kN; a = 30°, 0 = 45° , B = 60° 1] What is the resultant moment of the five forces acting on the rod about point A? a) - 154.8 kN.m b) 111.9 KN.m c) - 174.6 kN.m d) 162.9 kN.m e) 214.1 kN.m 0-47.1 kN.m 2] What is the resultant moment of the five forces acting on the rod about point B? | a) - 209.3 kN.m b) 215.7 kN.m c) 311.6 kN.m d) - 98.9 kN.m e) 125.4 kN.m f) - 124.2 kN.m 3] What is the resultant moment of the five forces acting on the rod about point C? a) - 204 kN.m b) 121 kN.m c) 146 kN.m d) - 279 kN.m e) 241 kN.m D- 353 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) – 212.7 kN.m b) 182.7 kN.m e) - 21.9 kN.m d) 36.9 kN.m e) - 27.1 kN.m ) 30.1 kN.m 5] What is the moment of the force F2 about point E? a) 100.3 kN.m b) 118.1 kN.m c) 224.6 kN.m d) 193.1 kN.m e) 151.1 kN.m ) 221.3 kN.m E.arrow_forward
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