Two forces act at a point in directions inclined to each other at 120. If the bigger force is 5N, and their resultant is at right angles to the smaller force, find the resultant and the smaller force.
 

Asked by lekhakarthikeyan | 29th May, 2017, 11:18: PM

Expert Answer:

 
begin mathsize 12px style Let space the space bigger space force space be space straight F subscript 1 space and space the space smaller space force space be space straight F subscript 2 space which space are space acting space at space angle space of space 120 degree.
Given space that space straight F subscript 1 space equals space 5 straight N space and space straight beta space equals space 90 degree space and space straight alpha space plus space straight beta space equals space 120 degree
therefore space straight alpha space equals space 120 degree space minus space 90 degree space equals space 30 degree
First comma space we space find space the space component space of space straight F subscript 1 space using space the space formula
straight F subscript 1 space equals space fraction numerator straight F space sinβ over denominator sin space left parenthesis straight alpha space plus space straight beta right parenthesis end fraction
rightwards arrow straight F space equals space fraction numerator straight F subscript 1 space sin space left parenthesis straight alpha space plus space straight beta right parenthesis over denominator sinβ end fraction
space space space space space space equals space fraction numerator 5 space cross times space sin space 120 degree over denominator sin space 90 degree end fraction
rightwards arrow straight F space equals space fraction numerator 5 space cross times 0.866 over denominator 1 end fraction
therefore straight F space equals space 4.33 space straight N
Component space straight F subscript 2 space can space be space found space using space the space same space formula.
straight F subscript 2 space equals space fraction numerator straight F space sinα over denominator sin space left parenthesis straight alpha space plus space straight beta right parenthesis end fraction
rightwards arrow space equals space fraction numerator 4.33 space cross times space sin space 30 degree over denominator sin space 120 degree end fraction
therefore space straight F subscript 2 space equals space space fraction numerator 4.33 space cross times 0.5 over denominator 0.866 end fraction space
therefore space straight F subscript 2 space equals space 2.5 space straight N
end style

Answered by Yashvanti Jain | 30th May, 2017, 11:24: AM