Given the following system, express each force as a Cartesian force vector.F₂ = 175 lbF₁ = 250 lbeto.ed3³640⁰45°120⁰60°F3 = 120 lb

From the given figure, it is clear that force makes and angle with x-axis and with xy-plane.First…

Answered: Given the following system, express…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Concept explainers

Question

Given the following system, express each force as a Cartesian force vector.
F₂ = 175 lb
F₁ = 250 lb
eto.ed3³6
40⁰
45°
120⁰
60°
F3 = 120 lb

Expert Solution

Step 1: Write force F1 in vector form.

From the given figure, it is clear that force $F subscript 1$ makes and angle $40 degree$ with x-axis and $30 degree$ with xy-plane.

First resolve force $F subscript 1$ onto xy-plane and z-axis. Thus,
i) z-component of force is
$table row cell F subscript 1 z end subscript end cell equals cell F subscript 1 sin 30 degree end cell row blank equals cell 250 space lb cross times sin 30 degree end cell row blank equals cell 125 space lb end cell end table$
ii) component along xy-plane is
$table row cell F subscript 1 comma x y end subscript end cell equals cell F subscript 1 cos 30 degree end cell row blank equals cell 250 space lb cross times cos 30 degree end cell row blank equals cell 216.51 space lb end cell end table$

Now resolve the component along xy-plane along x and y axis.
i) x-component of force is
$table row cell F subscript 1 x end subscript end cell equals cell F subscript 1 comma x y end subscript cos 40 degree end cell row blank equals cell 216.51 space lb cross times cos 40 degree end cell row blank equals cell 165.86 space lb end cell end table$
ii) y-component of force is
$table row cell F subscript 1 y end subscript end cell equals cell negative F subscript 1 comma x y end subscript sin 40 degree end cell row blank equals cell negative 216.51 space lb cross times sin 40 degree end cell row blank equals cell negative 139.17 space lb end cell end table$
Here negative sign indicates that force component acts along negative y-axis.

Write expression for force $F subscript 1$ in cartesian vector form.
$table row cell F with bar on top subscript 1 end cell equals cell F subscript 1 x end subscript i with hat on top plus F subscript 1 y end subscript j with hat on top plus F subscript 1 z end subscript k with hat on top end cell row cell F with bar on top subscript 1 end cell equals cell 165.86 i with hat on top minus 139.17 j with hat on top plus 125 k with hat on top space open square brackets lb close square brackets end cell end table$

Step by step

Solved in 4 steps with 27 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Design of Power Transmission Elements and Power Transmission Systems

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.

Similar questions