Final answer:
To find the resultant of two forces of 10N and 20N at an angle of 120 degrees, we can use vector addition. The magnitude of the resultant force is 29.1N and the direction is approximately -79.6°.
Step-by-step explanation:
To find the resultant of two forces, 10N and 20N, acting at an angle of 120 degrees to each other, we can use vector addition. We can split each force into its x and y components, and then add the corresponding components together. Let's assume the force of 10N is acting in the positive x-direction:
- F₁x = 10N * cos(120) = -5N
- F₁y = 10N * sin(120) = 8.66N
Now, let's assume the force of 20N is acting in the positive y-direction:
Adding the x-components and y-components separately, we get:
- Fx = F₁x + F₂x = -5N + 0N = -5N
- Fy = F₁y + F₂y = 8.66N + 20N = 28.66N
To find the magnitude of the resultant force, we can use the Pythagorean theorem:
- |Ftot| = √(Fx² + Fy²) = √((-5N)² + (28.66N)²) = √(25N² + 821.3956N²) = √846.3956N² = 29.1N
The magnitude of the resultant force is 29.1N. The direction can be found using the inverse tangent formula:
- θ = tan^(-1)(Fy / Fx) = tan^(-1)(28.66N / -5N) ≈ -79.6°
The direction of the resultant force is approximately -79.6° with respect to the positive x-axis.