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Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to solve the following problems. Determine the magnitude of the resultant R and the angle e between the x-axis and the line of action of the resultant for the following: 500 lb 700 lb 30° 55° 350 lb

Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to solve the following problems. Determine the magnitude of the resultant R and the angle e between the x-axis and the line of action of the resultant for the following: 500 lb 700 lb 30° 55° 350 lb

Elements Of Electromagnetics
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
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Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to solve the following problems. Determine the magnitude of the resultant R and the angle e between the x-axis and the line of action of the resultant for the following: 500 lb 700 lb 30° 55° 350 lb
Transcribed Image Text:Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to solve the following problems. Determine the magnitude of the resultant R and the angle e between the x-axis and the line of action of the resultant for the following: 500 lb 700 lb 30° 55° 350 lb
Expert Solution
Step 1

Given:

  • The magnitude of force one is F1 = 500 lb
  • The magnitude of force two is F2 = 700 lb
  • The magnitude of force three is F3 = 350 lb
  • The angle of force one from Y axis is ϕ = 30 °
  • The angle of force two from Y axis is ꝩ = 30 °
Step 2

The force diagram is given as,

Mechanical Engineering homework question answer, step 2, image 1

Step 3

The component the force in X direction can be calculated as,

Mechanical Engineering homework question answer, step 3, image 1

Substitute the known values in above equation,

Mechanical Engineering homework question answer, step 3, image 2

The component the force in Y direction can be calculated as,

Mechanical Engineering homework question answer, step 3, image 3

Substitute the known values in above equation,

Mechanical Engineering homework question answer, step 3, image 4

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