Three forces - F1, F2 and F3 - act on a base ring. Find: (1) Rmag, the magnitude

Question

Three forces - F1, F2 and F3 - act on a base ring.

Find:
(1) Rmag, the magnitude of the resultant force
(2) aR, the angle of the resultant force in radians

F1 = 100 lb

a1 = 33 deg

F2 = 40 lb

a2 = 58 deg

F3 = 59 lb

a3 = 90 deg

100% E Tue Jan 19 7:10 PM a E ] Safari File Edit View History Bookmarks Window Help 8 4) , egr.msu.edu Homework Chegg Study Guided Solutions and Study Help Chegg.com Three forces F1, F2 and F3 act on a base ring. - Google Search CE 221 Statics Evaluate Your Progres Home Review Lecture Practice Homework Sample Exams Syllabus ducs Evaluate Your Progress Logout Resultant of 3 forces Three forces F1, F2 and F3-act on a base ring Find: (1) Rmag, the magnitude of the resultant force (2) aR, the angle of the resultant force in radians a1 F1 Answer all numeric solutions with five significant figures. F1 100 lb Copyright 2015 CMl and Enwironmental Engineering Michigan State University Mackinac Bridge by Matthewjs007 CC BY a1 = 33 deg F2 = 40 lb a2 = 58 deg F3 = 59 lb a3 = 90 deg Contact the Staff

Explanation / Answer

Lets Consider all X- and Y- Components for all three forces

FX = Sqrt( F1x^2+F2x^2+F3x^2)

FX = Sqrt((100 Cos(360-33)) ^2 +( 40 Cos(90+58)) ^2 + 59 (Cos(90)) ^2))

Fx = Sqrt ( 83.867^2 +33.921^2+0)

Fx =90.467 lb

Similiary ,

FXY= Sqrt( F1y^2+F2y^2+F3y^2)

FXY= Sqrt((100 Cos(180+57)) ^2 +( 40 Cos(58)) ^2 + (59 (Cos(0) )^2))

Fy = Sqrt ( 2966.316+ 449.303+ 3481)

Fy = 83.045 lb

Resultant Force

Fmag = Sqrt ( 90.467^2+83.045^2)

Fmag = 122.80 lb

Angle = tan inverse (83.045/90.467)

= 42.551 degrees = 267.22 Radians

with repect to X axis Counter clockwise.

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