if the resultant of 2 equal force inclint to each other at 60° is 8root3N. Find the component forces?
To find the component forces, we can use trigonometry. Let's break down the given information step by step:
1. We are given that the resultant of the two equal forces is 8root3N. This implies that the magnitude of each force is half of the resultant, which is (8root3N)/2 = 4root3N.
2. We are also given that the forces are inclined to each other at an angle of 60°.
To find the component forces, we need to determine the horizontal and vertical forces separately using trigonometric functions:
Let's consider the horizontal component force:
Using the angle of 60°, we can determine the cosine of the angle:
cos(60°) = adjacent/hypotenuse
cos(60°) = horizontal force / 4root3N
Now, solving for the horizontal force:
horizontal force = cos(60°) * 4root3N
Similarly, let's consider the vertical component force:
Using the angle of 60°, we can determine the sine of the angle:
sin(60°) = opposite/hypotenuse
sin(60°) = vertical force / 4root3N
Now, solving for the vertical force:
vertical force = sin(60°) * 4root3N
Thus, the component forces are:
Horizontal force = cos(60°) * 4root3N
Vertical force = sin(60°) * 4root3N
These equations will allow you to calculate the horizontal and vertical forces based on the given information.