Two forces 5 newton and 4 newton are inclined to each other at 30° find the resultant and unknown angle
To find the resultant force and the unknown angle between the two forces, you can use vector addition.
Step 1: Resolve the forces into their x and y components.
Let's call the 5 N force F1 and the 4 N force F2.
F1x = F1 * cos(30°)
= 5 N * cos(30°)
≈ 4.33 N
F1y = F1 * sin(30°)
= 5 N * sin(30°)
≈ 2.5 N
F2x = F2 * cos(0°) (since the second force is already along the x-axis)
= 4 N * 1
= 4 N
F2y = F2 * sin(0°) (since the second force is already along the x-axis)
= 4 N * 0
= 0 N
Step 2: Add the x and y components separately.
Rx = F1x + F2x
= 4.33 N + 4 N
≈ 8.33 N
Ry = F1y + F2y
= 2.5 N + 0 N
= 2.5 N
Step 3: Calculate the magnitude and angle of the resultant force.
Resultant Force, R = √(Rx^2 + Ry^2)
= √((8.33 N)^2 + (2.5 N)^2)
≈ √(69.39 N^2 + 6.25 N^2)
≈ √(75.64 N^2)
≈ 8.7 N (approximately)
Angle, θ = arctan(Ry / Rx)
= arctan(2.5 N / 8.33 N)
≈ 16.6° (approximately)
Therefore, the resultant force is approximately 8.7 N, and the unknown angle is approximately 16.6°.