Statics and Mechanics of Materials
2nd Edition
ISBN: 9780073398167
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David Mazurek
Publisher: McGraw-Hill Education
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Chapter 3.2, Problem 34P
To determine
The value of
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Given the vectors P 3i - j + k, Q = 4i + Qyj - 2k, and S 2i - 2j + 2k, determine the value of Qy for which the three vectors are coplanar.
Given the Position vector
R= 2i -j+ 3k (m)
and the Force vector
F = i+j+k (kN)
Determine the angle in degrees between the two vectors.
Answer:
For the given vectors below, Solve for Vector č = (Ä + B) × (A· (B × A))
A = 3ỉ+ 23 - 6k
B = 3ỉ - 23 - 6 k
Chapter 3 Solutions
Statics and Mechanics of Materials
Ch. 3.1 - A 20-lb force is applied to the control rod AB as...Ch. 3.1 - A 20-lb force is applied to the control rod AB as...Ch. 3.1 - A 300-N force P is applied at point A of the bell...Ch. 3.1 - A 400-N force P is applied at point A of the bell...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 - 3.7 and 3.8 The tailgate of a car is supported by...Ch. 3.1 - 3.7 and 3.8 The tailgate of a car is supported by...Ch. 3.1 - 3.9 and 3.10 It is known that the connecting rod...Ch. 3.1 - 3.9 and 3.10 It is known that the connecting rod...
Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...Ch. 3.1 - Prob. 12PCh. 3.1 - Determine the moment about the origin O of the...Ch. 3.1 - Determine the moment about the origin O of the...Ch. 3.1 - Prob. 15PCh. 3.1 - Prob. 16PCh. 3.1 - Prob. 17PCh. 3.1 - A wooden board AB, which is used as a temporary...Ch. 3.1 - Prob. 19PCh. 3.1 - A small boat hangs from two davits, one of which...Ch. 3.1 - Prob. 21PCh. 3.1 - In Prob. 3.16, determine the perpendicular...Ch. 3.1 - In Prob. 3.16, determine the perpendicular...Ch. 3.1 - In Prob. 3.20, determine the perpendicular...Ch. 3.2 - Given the vectors P=3i-j+2k,Q=4i+5j-3k, and...Ch. 3.2 - Prob. 26PCh. 3.2 - Knowing that the tension in cable AC is 1260 N,...Ch. 3.2 - Knowing that the tension in cable AD is 405 N,...Ch. 3.2 - Three cables are used to support a container as...Ch. 3.2 - Three cables are used to support a container as...Ch. 3.2 - The 20-in. tube AB can slide along a horizontal...Ch. 3.2 - Solve Prob. 3.31 for the position corresponding to...Ch. 3.2 - Prob. 33PCh. 3.2 - Prob. 34PCh. 3.2 - Knowing that the tension in cable AB is 570 N,...Ch. 3.2 - Prob. 36PCh. 3.2 - A farmer uses cables and winch pullers B and E to...Ch. 3.2 - Solve Prob. 3.37 when the tension in cable AB is...Ch. 3.2 - To lift a heavy crate, a man uses a block and...Ch. 3.2 - Prob. 40PCh. 3.2 - Prob. 41PCh. 3.2 - Prob. 42PCh. 3.2 - Prob. 43PCh. 3.2 - A sign erected on uneven ground is guyed by cables...Ch. 3.2 - The frame ACD is hinged at and D and is supported...Ch. 3.2 - In Prob. 3.45, determine the moment about the...Ch. 3.2 - Prob. 47PCh. 3.2 - Prob. 48PCh. 3.3 - Two parallel 60-N forces are applied to a lever as...Ch. 3.3 - A plate in the shape of a parallelogram is acted...Ch. 3.3 - Prob. 51PCh. 3.3 - Prob. 52PCh. 3.3 - Four 112-in. -diameter pegs are attached to a...Ch. 3.3 - Prob. 54PCh. 3.3 - Prob. 55PCh. 3.3 - Prob. 56PCh. 3.3 - Replace the two couples shown with a single...Ch. 3.3 - Prob. 58PCh. 3.3 - Shafts A and B connect the gear box to the wheel...Ch. 3.3 - Prob. 60PCh. 3.3 - Prob. 61PCh. 3.3 - The force P has a magnitude of 250 N and is...Ch. 3.3 - Prob. 63PCh. 3.3 - A 260-lb force is applied at A to the rolled-steel...Ch. 3.3 - Prob. 65PCh. 3.3 - A force and couple act as shown on a square plate...Ch. 3.3 - Prob. 67PCh. 3.3 - Prob. 68PCh. 3.3 - Prob. 69PCh. 3.3 - Replace the 150-N force by an equivalent...Ch. 3.3 - Prob. 71PCh. 3.3 - Prob. 72PCh. 3.4 - A 4-m-long beam is subjected to a variety of...Ch. 3.4 - Prob. 74PCh. 3.4 - Determine the single equivalent force and the...Ch. 3.4 - The weights of two children sitting at ends A and...Ch. 3.4 - Prob. 77PCh. 3.4 - Prob. 78PCh. 3.4 - Four forces act on a 700375 -mm plate as shown....Ch. 3.4 - Prob. 80PCh. 3.4 - Prob. 81PCh. 3.4 - A truss supports the loading shown. Determine the...Ch. 3.4 - A machine component is subjected to the forces and...Ch. 3.4 - Solve Prob. 3.83, assuming that P=60N.Ch. 3.4 - Prob. 85PCh. 3.4 - Prob. 86PCh. 3.4 - Prob. 87PCh. 3.4 - Prob. 88PCh. 3.4 - Prob. 89PCh. 3.4 - Assuming e 600 in Prob. 3.89, replace the two...Ch. 3.4 - A blade held in a brace is used to tighten a screw...Ch. 3.4 - Prob. 92PCh. 3.4 - Four signs are mounted on a frame spanning a...Ch. 3.4 - Prob. 94PCh. 3.4 - Prob. 95PCh. 3.4 - Three children are standing on a 55-m raft. The...Ch. 3 - For the shift lever shown, determine the magnitude...Ch. 3 - Consider the volleyball net shown. Determine the...Ch. 3 - A crane is oriented so that the end of the 25-m...Ch. 3 - The 25-m crane boom AO lies in the yz plane....Ch. 3 - A single force P acts at C in a direction...Ch. 3 - While tapping a hole, a machinist applies the...Ch. 3 - A 500-N force is applied to a bent plate as shown....Ch. 3 - Prob. 104RPCh. 3 - Prob. 105RPCh. 3 - Prob. 106RPCh. 3 - Prob. 107RPCh. 3 - A regular tetrahedron has six edges of length a. A...
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- Given the Position vector Ř = i+j+3k (m) and the Force vector F = i - 7j + 2k (kN Determine the angle in degrees between the two vectors. Answer:arrow_forwardGiven the three vectors A = i, B = i- j, and C = k Find A.(BXC).arrow_forwardFind the projection of the vector A=-2j+k^ on the vector B= 6i+4 j+8k^arrow_forward
- Given the Position vector R= 5i + 4j + 3k (m) and the Force vector F = 4i – 5j+3k (kN) Determine the angle in degrees between the two vectors. Answer:arrow_forwardQ1/ Given the vectors 7 = 31-j+k and 7 = 2i - 3j+ k, find the product x and verify that this vector is orthogonal to and u. Also, find the 7x7 and compare it with x X vectorarrow_forward2. 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. SxParrow_forward
- Given the vectors P=3i- j +2k, Q= 4i+5j -3k, and S=-2i+3j -k, compute the scalar products P · Q, P · S, and Q · S.arrow_forwardThe moment of the force F=960-lb about the point O in Cartesian vector form is. F 1 ft 4 ft 2 ft A 4 ft. Select one: O a. Mo = 1600j – 3200k O b. Mo = -200j + 400k %3D O c. Mo = -200j - 400k %3D O d. Mo = 200j + 400k %3Darrow_forwardThe moment of the force F-480-lb about the point O in Cartesian vector form is. 1 ft> B 4 ft 2 ft 4 ft Select one: O a. Mo = 800;- 1600k O b. Mo = -200j + 400k Oc. Mo =-200j- 400k Od. Mo 200j + 400k EN Garrow_forward
- The moment of the force F=360-lb about the point O in Cartesian vector form is. 1 ft OB 4 ft' 2 ft 4 ft. Select one: 1200/-arrow_forwardFor the given vectors V₁ and V₂, determine V₁ + V₂, V₁ + V2, V₁ - V2, V₁ × V2, V₁ V₂. Consider the vectors to be nondimensional. Assume V₁ = 15, V₂ = 18, a = 3, b = 4,0 = 30°. V V₁ a Answers: V₁ + V₂ = i V₁ + V₂ = (i j+ k) V₁-V₂ = (i j+ i k) V₁x V₂ = (i i k) V1 V₂ = i i+ i i+ i i+ i +arrow_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
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