Explanation Given: The magnitude of force, F 1 = 700 lb . The magnitude of force, F 2 = 600 lb . The magnitude of force, F 3 = 800 lb . The angle between F 3 and z axis is γ 3 = 60 ° . The angle between F 3 and y axis , β 3 = 45 ° . The angle between F 1 and x axis is 30 ° The angle between F 3 and x axis, α 3 = 120 ° . Show the magnitude of components force F 1 into x , y , and z direction as in Figure (1). Show the magnitude of components force F 2 into x , y , and z direction as in Figure (2). Show the magnitude of components force F 3 into x , y , and z direction as in Figure (3). Express the force F 1 as a Cartesian vector using Figure (1). F 1 = F 1 x ( + i ) + F 1 y ( + j ) + F 1 z ( + k ) = F 1 cos 30 ° i + F 1 sin 30 ° j + 0 = F 1 [ cos 30 ° i + sin 30 ° j ] (I) Express the force F 2 as a Cartesian vector using Figure (2). F 2 = F 2 x ( + i ) + F 2 y ( + j ) + F 2 z ( + k ) = 0 i + F 2 cos θ j + F 2 sin θ k = F 2 [ cos θ j + sin θ k ] (II) Use Figure (2) to calculate the cos θ and sin θ . cos θ = 4 5 sin θ = 3 5 Express the force F 3 as a Cartesian vector using Figure (3). F 3 = F 3 x ( + i ) + F 3 y ( + j ) + F 3 z ( + k ) = F 3 cos 120 ° i + F 3 cos 45 ° j + F 3 cos 60 ° k = F 3 [ cos 120 ° i + cos 45 ° j + cos 60 ° k ] (III) Express the resultant force as a Cartesian vector. F R = F 1 + F 2 + F 3 (IV) Express the magnitude of F R . F R = ( F R ) x 2 + ( F R ) y 2 + ( F R ) z 2 (V) Write the coordinate direction angles. cos α = ( F R ) x F R (VI) cos β = ( F R ) y F R (VII) cos γ = ( F R ) z F R (VIII) Conclusion: Substitute 700 lb for F 1 in Equation (I). F 1 = 700 lb [ cos 30 ° i + sin 30 ° j ] = 700 lb [ 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 2.6, Problem 82P

To determine

The magnitude of resultant force FR and its coordinate direction angles (α,β,γ) on the eye bolt.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.6, Problem 81P

Chapter 2.6, Problem 83P

Students have asked these similar questions

Select the speed, feed and depth of the cut to turn wrought, low carbon steel (hardness of 200 BHN) on lathe with AISI tool material of HSS M2 or M3. (Hint: refer to Chapter 21 for recommended parameters).

Only question 1&2

Only question 3&4

Chapter 2 Solutions

Engineering Mechanics: Statics & Dynamics (14th 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 - Two forces act on the hook. Determine the...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 - The force F = 450 lb acts on the frame. Resolve...Ch. 2.3 - If force F is to have a component along the u axis...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.

The magnitude of resultant force F R and its coordinate direction angles ( α , β , γ ) on the eye bolt.

Solution Summary: The author explains the magnitude of the resultant force F_R and its coordinate direction angles on the eye bolt.

Videos

The magnitude of resultant force FR and its coordinate direction angles (α,β,γ) on the eye bolt.

Want to see the full answer?

Chapter 2 Solutions