<LCPO> VECTOR MECH,STAT+DYNAMICS
12th Edition
ISBN: 9781265566296
Author: BEER
Publisher: MCG
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Chapter 3.2, Problem 3.35P
Given the
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a = 4 mb = 3.2 mc = 2 mF = {-7i+4j+12k} NSpecified axis: AF
Find the following:
Find the z-component of the moment of F about the specified axis.
Find the x-component of the moment of F about the specified axis.
Find the magnitude of the moment of F about the specified axis.
Find the y-component of the moment of F about the specified axis.
For the given vectors below, Solve for Vector č = (Ä + B) × (A· (B × A))
A = 3ỉ+ 23 - 6k
B = 3ỉ - 23 - 6 k
2. Given the vectors, compute the following:
P= i+j+ 2k
A. Scalar products
1. Q.S
Q = 3i + 4j + 5k
B. Vector products
1. PxQ
S= 4i + 3j + 2k
C. Mixed Triple products
1. Q. (S x P)
2. P. (Qx S)
2. SxP
Chapter 3 Solutions
<LCPO> VECTOR MECH,STAT+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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- Find the desired ones by randomly typing two A and B vectors in the form below. A = (5) i + (7) j + (10) k B = (2) i + (3) j + (5) k The cross product A x B =? Scalar product A x B =? Intensity A x B =?arrow_forwardThe moment of the force F=180-lb about the point O in Cartesian vector form is. 1 ft 4 ft 2 ft 4 ft. Select one: O a. Mo = 300j – 600OK O b. Mo = -200j + 400k O . Mo = -200j – 400k O d. Mo = 2003 + 400karrow_forwardProblem 4 From the figure, w1 =13kN/m, w2=10kN/m, F1 =7kN 1. Find the resultant of the forces 2. Find the location of the resultant from point B. 7m 4m 2marrow_forward
- 4- Two non-zero vectors A =i-j+2k and B = 2i-j+k are neither orthogonal nor parallel.arrow_forwardThe moment of the force F=960-lb about the point O in Cartesian vector form is. 1 ft 4 ft 2ft Select one: O a. Mo = 1600 – 3200A O b. Mo = -200j + 400k Oc. Mo =-200; – 400k O d. Mo= 200; + 400k 1:15 PMarrow_forwardThe moment of the force F=120 lb about the point O in Cartesian vector form is. F= 120 lb 1 ft 4 ft 2 ft 4 ft Select one: O a. Mo = 200j – 400k O b. Mo = -2007 + 400k O c. Mo = -2007j – 400k O d. Mo = 200j + 400k ENarrow_forward
- 1. Please refer to the following vectors:A = 6i + 2j - 3kB = 3i - j - 2kC = -i + j - 4kD = j - 3kE = -i + 2kF = -5kG = 2iH = -3jI = -4i +4j Two airplanes started drifting away from the origin along the directions of displacement vectors {B} km and {E} km respectively. If vectors B and E are their position vectors in rectangular coordinate system after some time t, what will be their separation distance in kilometers? 2. A ball is speeding up along a circular track. What can be said about the velocity and acceleration vectors on the body? 3. In an intersection, a bus moving at (100i) m/s and a truck moving at (200j) m/s collided with each other. Assuming that the two objects have the same mass, what would be their final speed together?arrow_forwardemploy scalar analysis the scalar component of the vector F. find the vector moment that is formed from the force vector F on the point of O as well as the magnitude of the momentarrow_forwardQ 3. A frame B is rotated 90 degree about the z-axis, then translated 3 and 5 units relative to the n- and o-axes respectively, then rotated another 90 degree about the n-axis, and finally, 90 degree about the y-axis. Find the new location and orientation of the frame. O 1 0 1 1 0 1 B = - 1 1 1arrow_forward
- Example: The resultant of the concurrent forces shown in figure is 300 N pointing up along the y-axis. Compute the value of F and e required to give this resultant. 50ON 30 240N o Since the resultant is up along y- axis then EF = 0 o HW. o F = Fcos 0 + 240 cos 30 – 500 = 0 o Fcos 0- 292.15 = 0 o Repeat this problem if the resultant is 40ON down to the right at 60° with the x-axis. o Also repeat the problem if the body is in equilibrium. o Fcos 0 = 292.15... .... (1) o F, = R = Fsin 0 - 240 sin 30 = 300 Fsin 0 = 300+ 120 = 420 ..... (2) Divide eqn. (2) by (1) yields F sin 0 420 %3D F cos e 292.15 o tan 0 = 1.4376, 0 = tan 1.4376 = 55.18° 420 F = sin 55.18 = 511.6Narrow_forwardFind the following for the vectors v = 10i+11j-2k and u=8i + 15j. a. v. u, |v|, |u| b. the cosine of the angle between v and u c. the scalar component of u in the direction of v d. the vector proj, u a. v. u= (Type an exact answer, using radicals as needed.) |v|= (Type an exact answer, using radicals as needed.) |u| = [ (Type an exact answer, using radicals as needed.) b. The cosine of the angle between v and u is (Type an exact answer, using radicals as needed.) c. The scalar component of u in the direction of v is (Type an exact answer, using radicals as needed.) d. proj, u = (Type your answer in terms of i, j, and k. Type an exact answer, using radicals as needed.)arrow_forwardTwo vectors A and B are acting as shown in figure. If A = resultant is: 10 N 60° 10 N B 10 N then thearrow_forward
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