Question

The resultant of two forces at right angle is 5N. When the angle between them is 120 degrees the resultant is root 13, then find the magnitudes of two forces.

Answer 1

Answer:

What is force?

• A force is an influence that can change the motion of an object
• A force can cause a body with mass to change speed, i.e accelerate.
• Force can also be intuitively described as push or pull.
• A force has both magnitude and direction making its a vector quantity.

Explanation:

Given:- R1=5N

            angle 1 = 90^.

            R2= root 13

            angle 2= 120^.

to find :- magnitude

solution:- a and b two forces

             (a+b)^2 = R1^2

             a^2 + b^2 + 2abcos(angle 1) = 25

             a^2 + b^2 + 2abcos(90) = 25

              a^2 + b^2 = 25

next

              a^2 + b^2 + 2abcos(120) = (root 13)^2

              a^2 + b^2 + 2ab(-1/2) = 13

              a^2 - b^2 = 13

              25 - 13 = ab

               12 = ab --------- 1

            applying

          (a + b)^2 = a^2 + b^2 + 2ab

                         = 25 + 2*12

                        = 49

           a + b = 7 ----------- 3

using 2 in 3

12/b + b = 7

12 + b^2 = 7b

b^2 - 7b + 12 = 0

b^2 - 4b - 3b + 12 = 0

(b - 4)(b - 3) = 0  

b = 3,4

hence a = 3N

           b = 4N  

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