Explanation Given information: The force F is 100 lb . Calculation: Establish a position vector from B to C and B to A . The coordinates are: A ( − 3 , 0 , 0 ) ft , B ( 0 , 0 , 0 ) ft , and C ( 6 , 4 , − 2 ) ft . Calculate the position vector r in the direction of BC is r B C . r B C = ( x C − x B ) i + ( y C − y B ) j + ( z C − z B ) k (1) Here, the coordinates of B and C in the x , y and z directions are x B , x C , y B , y C , z B , and z C , respectively. Calculate the length of the cable B C is r B C . r B C = ( x C − x B ) 2 + ( y C − y B ) 2 + ( z C − z B ) 2 (2) Calculate the position vector r in the direction of BA is r B A . r B A = ( x A − x B ) i + ( y A − y B ) j + ( z A − z B ) k (3) Here, the coordinates of A in the x , y and z directions are x A , y A , , and z A , respectively. Calculate the length of the cable B A is r B A . r B A = ( x A − x B ) 2 + ( y A − y B ) 2 + ( z A − z B ) 2 (4) Express the angle θ between the pipe segments B A and B C . θ = 180 ° − { cos − 1 [ r B C ⋅ r B A | r B C | | r B A | ] } (5) Conclusion: Substitute 6 ft for x C , 4 ft for y C , − 2 ft for z C , 0 ft for x B , 0 ft for y B , and 0 ft for z B in Equation (1). r B C = ( 6 − 0 ) i + ( 4 − 0 ) j + ( − 2 − 0 ) k = { 6 i + 4 j − 2 k } ft Substitute 6 ft for x C , 4 ft for y C , − 2 ft for z C , 0 ft for x B , 0 ft for y B , and 0 ft for z B in Equation (2)

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related t…

Videos

Question

Chapter 2.9, Problem 80P

To determine

Find the angle θ between the pipe segments BA and BC.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.9, Problem 79P

Chapter 2.9, Problem 81P

Students have asked these similar questions

Below is a projection of the inertia ellipsoid in the b1-b2 plane (b1 and b2 are unit vectors). All points on the ellipsoid surface represent moments of inertia in various directions. The distance R is related to the distance D such that R = md. Determine m.

Below is a projection of the inertia ellipsoid in the b1-b2 plane (b1 and b2 are unit vectors). All points on the ellipsoid surface represent moments of inertia in various directions. Determine I_aa ( moment of inertia) for direction n_a (this is a unit vector).

The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁

Chapter 2 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 2.3 - In each case, construct the parallelogram law to...Ch. 2.3 - In each case, show how to resolve the force F into...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - Resolve the force into components acting along...Ch. 2.3 - Prob. 6FP Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find the angle θ between the pipe segments B A and B C .

Solution Summary: The author calculates the angle theta between the pipe segments and the length of the cable BC.

Concept explainers

Videos

Find the angle θ between the pipe segments BA and BC.

Want to see the full answer?

Chapter 2 Solutions