Two forces of magnitude 8N make angles of 30°and120°with x axis magnitude of y component of resultant will be
8 sin 30 + 8 sin 120
8 (1/2) + 8 (1/2) sqrt 3
8cis30° + 8cis120° = 8√2 cis75°
or, 8<√3/2,1/2>+8<-1/2,√3/2> = 4<√3-1,√3+1>
either way, the y-component is 4(1+√3) ≈ 10.928
To find the magnitude of the y component of the resultant force, we need to calculate the individual y components of the given forces and then add them together.
Given:
Force 1 magnitude (F1) = 8 N
Force 1 angle with x-axis (θ1) = 30°
Force 2 magnitude (F2) = 8 N
Force 2 angle with x-axis (θ2) = 120°
To determine the y component of each force, we use trigonometry. The y component of a force can be found by multiplying the magnitude of the force by the sine of the angle it makes with the x-axis.
For Force 1:
y component of Force 1 (F1y) = F1 * sin(θ1)
For Force 2:
y component of Force 2 (F2y) = F2 * sin(θ2)
Now, we can calculate the magnitudes of the y components:
F1y = 8 N * sin(30°) = 4 N
F2y = 8 N * sin(120°) = 6.9282 N (rounded to four decimal places)
Finally, to find the magnitude of the y component of the resultant force (Fy), we add the y components of both forces:
Fy = F1y + F2y
= 4 N + 6.9282 N
= 10.9282 N (rounded to four decimal places)
Therefore, the magnitude of the y component of the resultant force is approximately 10.9282 N.