Explanation Given: The magnitude of the component vector force F 1 , F 1 = 350 N . The magnitude of the component vector force F 2 , F 2 = 100 N . The magnitude of the component vector force F 3 , F 3 = 250 N . Angle between F 2 and x -axis is 45 ° Angle between F 2 and y axis is 60 ° . Angle between F 3 and y axis is 45 ° . Angle between F 3 and x -axis is 60 ° . Angle between F 3 and z axis is 60 ° . Angle between F 1 and z axis is 40 ° . Angle between F 2 and z axis is 120 ° . Write the vector force F 1 in Cartesian vector form. F 1 = ( F 1 ) x i + ( F 1 ) y ( + j ) + ( F 1 ) z ( + k ) = 0 i + F 1 sin 40 ° ( + j ) + ( F 1 cos 40 ° ) ( + k ) (I) Here, the unit vectors are i , j , and k . Write the vector force F 2 in Cartesian vector form. F 2 = ( F 2 ) x i + ( F 2 ) y ( + j ) + ( F 2 ) z ( + k ) = ( F 2 cos 45 ° ) i + ( F 2 cos 60 ° ) ( + j ) + ( F 2 cos 120 ° ) ( + k ) (II) Here, the component force F 2 in x , y , and z axes are F 2 x , F 2 y , and F 2 z , respectively. Write the vector force F 3 in Cartesian vector form. F 3 = ( F 3 ) x i + ( F 3 ) y ( + j ) + ( F 3 ) z ( + k ) = ( F 3 cos 60 ° ) i + ( F 3 cos 135 ° ) ( + j ) + ( F 3 cos 60 ° ) ( + k ) (III) Here, the component force F 3 in x , y , and z axes are F 3 x , F 3 y , and F 3 z , respectively. Express the resultant force of vector force F 1 , F 2 , and F 3 . F R = F 1 + F 2 + F 3 (IV) Write the magnitude of the resultant force. F R = ( F R ) x 2 + ( F R ) y 2 + ( F R ) z 2 (V) Here, the magnitude of the resultant force measured along x , y , and z axes is ( F R ) x , ( F R ) y , and ( F R ) z . Determine 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 350 N for F 1 in Equation (I). F 1 = 0 i + ( 350 N ) ( 0.6427 ) ( + j ) + ( ( 350 N ) ( 0

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Question

Chapter 2.6, Problem 77P

To determine

The expression of each force (F1,F2,F3) in Cartesian vector form.

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.6, Problem 76P

Chapter 2.6, Problem 78P

Students have asked these similar questions

I submitted the below question and received the answer i copied into this question as well. Im unsure if it is correct, so looking for a checkover. i am stuck on the part tan-1 (0.05) = 0.04996 radians. Just unsure where the value for the radians came from. Just need to know how they got that answer and how it is correct before moving on to the next part. If any of the below information is wrong, please feel free to give me a new answer or an entire new explanation. An Inclining experiment done on a ship thats 6500 t, a mass of 30t was moved 6.0 m transvesly causing a 30 cm deflection in a 6m pendulum, calculate the transverse meta centre height. Here is the step-by-step explanation: Given: Displacement of the ship (W) = 6500 tonnes = 6500×1000=6,500,000kg Mass moved transversely (w) = 30 tonnes=30×1000=30,000kg The transverse shift of mass (d) = 6.0 meters Pendulum length (L) = 6.0 meters Pendulum deflection (x) = 30 cm = 0.30 meters Step 1: Formula for Metacentric Height…

Answer the assignment question, expert only

A 1 inch rod diameter B 3/4 inch rod diameter C 1/2 inch rod diameter D 3/8 inch rod diameter

Chapter 2 Solutions

Engineering Mechanics: Statics

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 this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6 Ch. 2.3 - Determine the magnitude of the resultant force FR...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...Ch. 2.3 - Determine the magnitude of the resultant force FR...

Knowledge Booster

The expression of each force ( F 1 , F 2 , F 3 ) in Cartesian vector form. The magnitude ( F R ) and coordinate direction angles of the resultant force acting on the screw eye ( α , β , and γ ) .

The expression of each force (F1,F2,F3) in Cartesian vector form. The magnitude (FR) and coordinate direction angles of the resultant force acting on the screw eye (α,β, and γ).

Want to see the full answer?

Chapter 2 Solutions

The expression of each force (F1,F2,F3) in Cartesian vector form.

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