Question

Two forces are such that the sum of their magnitude is 18n .Their resultant is root228 when they are at 120 then the magnitude of forces are

Answer 1

here is your answer hope it helps

Answer 2

Given:

Sum of forces given , A + B = 18N

Resultant of forces R = √228 N

angle between the forces = 120°

To Find:

find the magnitude of the forces

Solution:

as given in the question,

A + B = 18N ...........................(1)

Resultant of the forces acting at angle are given by,

R = √A² + B² + 2ABcosα

√228 = √{(A+B)² - 2AB+ 2ABcos 120}

cos 120 = -(1/2)

√228=√{(18²) - 2AB -AB}  

228 = 324 -3AB

3AB = 324 - 228

3AB = 96

AB = 96/3

AB =32 .......................................(2)

putting the value of AB in eq 1.

A + 32/A = 18

A² + 32 = 18A

A² - 18A +32 = 0

solving above equation we get ,

A = 2 and 16

So when A= 2N , then B =16N

  when A= 16N then B = 2N