two force of 20N and 34N act on a body in such a way that they make an angle of 35 with each other. find the resultant of the two force
Using the law of cosines, and the fact that adjacent angles of a parallelogram are supplementary,
r^2 = 20^2 + 34^2 + 2*20*34 cos35°
r^2 = 2670
1200N
To find the resultant of two forces, you can use the concept of vector addition. Vector addition involves combining the magnitudes and directions of the two forces to obtain the resultant force.
In this case, we have two forces of 20N and 34N with an angle of 35 degrees between them. To find the resultant, follow these steps:
Step 1: Split the forces into their horizontal and vertical components:
- Force 1 (20N): Its vertical component is calculated as 20N * sin(35°), and the horizontal component is 20N * cos(35°).
- Force 2 (34N): Its vertical component is 34N * sin(180° - 35°), and the horizontal component is 34N * cos(180° - 35°).
Step 2: Add the corresponding horizontal and vertical components of the forces:
- Vertical component: Sum the vertical components of both forces.
- Horizontal component: Sum the horizontal components of both forces.
Step 3: Use the horizontal and vertical components to find the magnitude and direction of the resultant force:
- Magnitude: Use the Pythagorean theorem, which states that the square of the resultant magnitude is equal to the sum of the squares of the vertical and horizontal components.
- Direction: Use trigonometry to find the angle of the resultant force. The angle can be obtained by using the inverse tangent function.
By following these steps, you can find the resultant force.