Ex 1
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Statics – Exercise No. 1 2.96 (a) Express the weight W required to maintain equilibrium in terms of P, d, and h. (b) For W = 800 N, P = 200 N, and d = 600 mm, determine the value of h consistent with equilibrium.
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2 Answer: (a) W = P 2 1 + d h ; (b) h = 75.6 mm.
2.100 A container is supported by three cables as shown. Determine the weight W of the container, knowing that the tension in cable AB is 500 N. Answer: W = 1210 N.
3.27 Given the vectors P = 2i + 3j – k, Q = 5i – 4j + 3k, and S = -3i + 2j – 5k, compute the scalar products P∙Q, P∙S, and Q∙S. Answer: P∙Q = -5 ; P∙S = 5 ; Q∙S = -38. 3.28 From the scalar product P1∙P2 and use the result obtained to prove the identity cos(θ1 − θ 2 ) = cos θ1 cos θ 2 + sin θ1 sin θ 2 .
3.31 Knowing that the tension in cable AC is 945 N, determine (a) the angle between cable AC and the boom, (b) the projection on AB of the force exerted by cable AC at point A. Answer: (a) θ = 59.10 ; (b) Fon AB = 486 N.
3.35 Given the vectors P = 2i + 3j – k, Q = 5i – 4j + 3k, and S = -3i + 2j – 5k, compute P∙(Q×S), (P×Q)∙S and (S×Q)∙P. Answer: P∙(Q×S) = 78 ; (P×Q)∙S = 78 ; (S×Q)∙P = -78. 3.36 Given the vectors P = 4i - 2j + 3k, Q = 2i + 4j - 5k, and S = 7i - j + SZk, determine the value of SZ for which the tree vectors are coplanar. Answer: SZ = 2. 1
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All the questions are taken from Ferdinand P. Beer and E. Russell Johnston Jr. “Vector Mechanics for Engineers, Statics” Second SI Metric Edition, McGraw-Hill Book Company.
( )
2 Answer: (a) W = P 2 1 + d h ; (b) h = 75.6 mm.
2.100 A container is supported by three cables as shown. Determine the weight W of the container, knowing that the tension in cable AB is 500 N. Answer: W = 1210 N.
3.27 Given the vectors P = 2i + 3j – k, Q = 5i – 4j + 3k, and S = -3i + 2j – 5k, compute the scalar products P∙Q, P∙S, and Q∙S. Answer: P∙Q = -5 ; P∙S = 5 ; Q∙S = -38. 3.28 From the scalar product P1∙P2 and use the result obtained to prove the identity cos(θ1 − θ 2 ) = cos θ1 cos θ 2 + sin θ1 sin θ 2 .
3.31 Knowing that the tension in cable AC is 945 N, determine (a) the angle between cable AC and the boom, (b) the projection on AB of the force exerted by cable AC at point A. Answer: (a) θ = 59.10 ; (b) Fon AB = 486 N.
3.35 Given the vectors P = 2i + 3j – k, Q = 5i – 4j + 3k, and S = -3i + 2j – 5k, compute P∙(Q×S), (P×Q)∙S and (S×Q)∙P. Answer: P∙(Q×S) = 78 ; (P×Q)∙S = 78 ; (S×Q)∙P = -78. 3.36 Given the vectors P = 4i - 2j + 3k, Q = 2i + 4j - 5k, and S = 7i - j + SZk, determine the value of SZ for which the tree vectors are coplanar. Answer: SZ = 2. 1
1
All the questions are taken from Ferdinand P. Beer and E. Russell Johnston Jr. “Vector Mechanics for Engineers, Statics” Second SI Metric Edition, McGraw-Hill Book Company.
