Two forces 15Nand 10N are inclined at 70° to each other find the resultant of forces
15 N in x direction
10 in Y direction
|F| = sqrt (225 + 100) = 18.0 N
tan theta = 10/15
theta = 33.7 degrees above x axis
To find the resultant of two forces, we can use vector addition. Here's how you can calculate the resultant of two forces inclined at an angle to each other:
1. Break down each force into its horizontal and vertical components. To do this, use trigonometry. Let's consider the 15N force first.
- The horizontal component of the 15N force can be calculated as 15N * cos(70°).
- The vertical component of the 15N force can be calculated as 15N * sin(70°).
Similarly, for the 10N force:
- The horizontal component of the 10N force can be calculated as 10N * cos(0°).
- The vertical component of the 10N force can be calculated as 10N * sin(0°).
2. Add up the horizontal and vertical components of both forces separately. This will give you the total horizontal and vertical components.
- The total horizontal component is the sum of the horizontal components of the two forces: (15N * cos(70°)) + (10N * cos(0°)).
- The total vertical component is the sum of the vertical components of the two forces: (15N * sin(70°)) + (10N * sin(0°)).
3. Use the Pythagorean theorem to find the magnitude of the resultant force. The magnitude is the square root of the sum of the squares of the total horizontal and vertical components:
- Resultant magnitude = √[(total horizontal component)^2 + (total vertical component)^2].
4. Find the direction or angle of the resultant force using trigonometry. The angle is the inverse tangent of the ratio of the total vertical component to the total horizontal component:
- Resultant angle = tan^(-1)(total vertical component / total horizontal component).
By following these steps, you can find the magnitude and direction of the resultant force.