two forces, one of 12 N and another of 24 N , act on a body in such a way that they make an angle of 90degree with each other. find the resultant of the two forces
To find the resultant of the two forces, we need to use the concept of vector addition. Here's how you can find the resultant:
1. Draw a diagram: Draw a coordinate system and represent the two forces as vectors. Label them as F1 and F2. In this case, F1 is 12 N and F2 is 24 N. Make sure to draw the vectors so that they form a right angle (90 degrees) with each other.
2. Resolve the forces: Resolve each force into its components along the x and y directions. To do this, use the trigonometric functions sine and cosine.
- For F1: Since it forms a 90-degree angle, its x-component will be F1 * cos(90°) = 0 N, and its y-component will be F1 * sin(90°) = 12 N.
- For F2: Its x-component will be F2 * cos(0°) = 24 N, and its y-component will be F2 * sin(0°) = 0 N.
3. Add the components: Add the x-components and y-components separately to find the total x-component and total y-component.
- Total x-component = x-component of F1 + x-component of F2 = 0 N + 24 N = 24 N.
- Total y-component = y-component of F1 + y-component of F2 = 12 N + 0 N = 12 N.
4. Use the Pythagorean theorem: Now that we have the total x-component and total y-component, we can find the magnitude of the resultant force using the Pythagorean theorem.
- Magnitude of the resultant force = √(Total x-component)^2 + (Total y-component)^2 = √(24 N)^2 + (12 N)^2 ≈ 26.83 N.
5. Find the direction: To find the direction of the resultant, use the inverse tangent function.
- Direction = tan^(-1)(Total y-component / Total x-component) = tan^(-1)(12 N / 24 N) ≈ 26.57°.
Therefore, the magnitude of the resultant force is approximately 26.83 N, and the direction is approximately 26.57°.