two forces of magnitude 8N making an angle of 30 and 120 with xaxis . the y component of resultant A/ O B/ 4N C/ 8N D/ 16N
8 sin 30 + 8 sin (180-120)
4 + 8 (.866) = 4+6.93 = 11 N
In other words none of the above
I bet you mean 30 and 150 with x axis in which case C
there is no option of 11N . i have tried to sole it dozen of times but i am unable to figure out the right option which is 8N. Can anyone tell me how i can solve it in right manner to get correct option
To find the y-component of the resultant force, we can use the formula for finding the resultant of two vectors at an angle:
Resultant force = √(F1^2 + F2^2 + 2F1F2cosθ)
Where F1 and F2 are the magnitudes of the two forces, and θ is the angle between them.
In this case, F1 = F2 = 8N, and the angles are 30° and 120°.
So, substituting the values into the formula, we get:
Resultant force = √((8^2 + 8^2 + 2(8)(8)cos30°) + (8^2 + 8^2 + 2(8)(8)cos120°))
Simplifying further:
Resultant force = √(64 + 64 + 128cos30° + 64 + 64 + 128cos120°)
Now, let's calculate the values of cos30° and cos120°:
cos30° = √3/2
cos120° = -1/2
Substituting these values into the equation:
Resultant force = √(128 + 128(√3/2) + 128(-1/2))
Simplifying further:
Resultant force = √(128 + 64√3 - 64)
Resultant force = √(192 - 64 + 64√3)
Resultant force = √(128 + 64√3)
Resultant force ≈ 16.97N
So, the y-component of the resultant force is approximately 16.97N.
So, the correct option is D/ 16N.