Two forces, whose resultant is 100N, are perpendicular to each other. if one of them make an angle of 60° with the resultant, calculate it's magnitude (sin60°=0.8660,cos60°=0.5000)
To solve this problem, we will use vector addition and trigonometry. Here's how you can calculate the magnitude of the force that makes an angle of 60° with the resultant:
1. Let's assume the magnitudes of the two perpendicular forces are A and B, with A making an angle of 60° with the resultant.
2. Since we know the resultant force is 100N, we can write the equation for the magnitude of the resultant as:
magnitude of resultant (R) = √(A^2 + B^2)
The above equation represents the Pythagorean theorem for right-angled triangles.
3. Now, we can utilize the fact that A makes an angle of 60° with the resultant force to set up a trigonometric equation. We can write:
A = R * sinθ
where θ is the angle between A and the resultant force.
In this case, we can substitute the given angle, θ = 60°, and the magnitude of the resultant, R = 100N, into the equation:
A = 100N * sin(60°)
4. Evaluating the sine of 60° using a calculator or by referring to a trigonometric table, we find:
A = 100N * 0.8660
5. Calculating further, we get:
A ≈ 86.60N
Therefore, the magnitude of the force (A) that makes an angle of 60° with the resultant force is approximately 86.60N.