Two forces 10N and 20N are inclined at an angle 60° to each other. Find the resultant force
To find the resultant force of two forces inclined at an angle to each other, you can use the concept of vector addition.
Step 1: Resolve each force into horizontal and vertical components.
For the 10N force:
Horizontal component: 10N * cos(60°) = 5N
Vertical component: 10N * sin(60°) = 8.660N (approx)
For the 20N force:
Horizontal component: 20N * cos(60°) = 10N
Vertical component: 20N * sin(60°) = 17.320N (approx)
Step 2: Add the horizontal and vertical components separately to find the resultant horizontal and vertical forces.
Horizontal component: 5N + 10N = 15N
Vertical component: 8.660N + 17.320N = 25.980N (approx)
Step 3: Use the Pythagorean theorem to find the magnitude of the resultant force.
Resultant force: √(15N^2 + 25.980N^2) ≈ √(225N^2 + 676.2N^2) ≈ √901.2N^2 ≈ 30N
Step 4: Use trigonometry to find the angle of the resultant force.
Angle of the resultant force = tan^(-1)(Vertical component / Horizontal component) ≈ tan^(-1)(25.98N / 15N) ≈ 59.04° (approx)
Therefore, the resultant force is approximately 30N and it makes an angle of approximately 59.04° with the horizontal axis.