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Grade 11General Physics

find the magnitude of resultant of following three forces acting on a particle.F1=20n in eastward direction,F2 =20n due north easr and F3=20n in southward direction

Profile image of ISHIKA
9 Years agoGrade 11
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2 Answers

Profile image of Soumya Ranjan Mohanty
9 Years ago
Hello,
you can solve this problem by plotting the free body diagram of the particle.
So as there are 3 forces acting on the particle i.e F1=20 N towards east, F2=20 N towards north east and F3=20 N towards south, so first lets find the resultant of F1 and F3 and lets say it F4.
SO F4=sqrt(F1^2+F3^2+2cos 90) = sqrt(20^2+20^2+0)=sqrt(800)=20*sqrt(2) and direction of F4=tan^-1 (20/20) =45 degrees between east and south i.e south east.
 
now les find resultant of F2 and F4. Direction between F2 and F4 is 90 degrees.
SO resultant=sqrt(F2^2+F4^2+2cos 90) = sqrt(400+800+0)=sqrt(1200)=20*sqrt(3)=20*1.732=34.64 N
 
THerefore, resultant of forces acting on the particle is 64.64 N.
Profile image of Soumya Ranjan Mohanty
9 Years ago
I mis-typed the answer on the last line, the resultant is 34.64 N. So, I am resposting it.
you can solve this problem by plotting the free body diagram of the particle.
So as there are 3 forces acting on the particle i.e F1=20 N towards east, F2=20 N towards north east and F3=20 N towards south, so first lets find the resultant of F1 and F3 and lets say it F4.
SO F4=sqrt(F1^2+F3^2+2cos 90) = sqrt(20^2+20^2+0)=sqrt(800)=20*sqrt(2) and direction of F4=tan^-1 (20/20) =45 degrees between east and south i.e south east.
 
now les find resultant of F2 and F4. Direction between F2 and F4 is 90 degrees.
SO resultant=sqrt(F2^2+F4^2+2cos 90) = sqrt(400+800+0)=sqrt(1200)=20*sqrt(3)=20*1.732=34.64 N
 
THerefore, resultant of forces acting on the particle is 34.64 N.

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