A force of 200N is resolve in two forces if one component is equal to 120N and makes an angle of 30¡ã with 200N force find the other force
To find the other force, we can use trigonometry and resolve the 200N force into its two components.
Let's denote the other force as F2.
Given:
Total force (F1) = 200N
One component (F1x) = 120N
Angle between F1 and F1x (θ) = 30°
Now, we can use trigonometry to find the other component (F1y) and the other force (F2).
Using the angle (θ) and the adjacent side (F1x), we can find the hypotenuse (F1) using the cosine function:
cos(θ) = F1x / F1
Rearranging the above equation, we get:
F1 = F1x / cos(θ)
Substituting the given values, we have:
F1 = 120N / cos(30°)
F1 ≈ 138.56N
Now, we can find the other component (F1y) using the Pythagorean theorem:
F1y = sqrt(F1^2 - F1x^2)
F1y = sqrt(138.56^2 - 120^2)
F1y ≈ 48.50N
Finally, to find the other force (F2), we need to subtract this component (F1y) from the total force (F1):
F2 = F1 - F1y
F2 = 138.56N - 48.50N
F2 ≈ 90.06N
Therefore, the other force (F2) is approximately 90.06N.
To find the other force, we need to resolve the 200N force into its two components: the 120N component and the unknown component. Let's call the unknown force X.
To resolve the force, we can use trigonometry. The 120N component is the adjacent side of a right triangle, and the 200N force is the hypotenuse. The angle between the 120N component and the 200N force is given as 30 degrees.
Now, we can use the cosine function to find the value of the unknown force X.
cos(30°) = adjacent/hypotenuse
cos(30°) = 120N/X
Rearranging the equation, we have:
X = 120N/cos(30°)
Now, we can solve for X by substituting the value of cos(30°) ≈ 0.866:
X = 120N/0.866
X ≈ 138.33N
Therefore, the value of the other force is approximately 138.33N.