Four forces act as 9n,15n,10n,12n, calculate their resultant
To calculate the resultant of multiple forces, you need to add all the forces together. Each force has both magnitude (strength) and direction.
Step 1: Draw a diagram:
Draw a vector for each force, representing its magnitude and direction. Label the forces with their respective magnitudes: 9N, 15N, 10N, and 12N. Make sure to draw the vectors in the correct direction.
Step 2: Break the forces into components:
Using basic trigonometry, break each vector force into its horizontal (x-axis) and vertical (y-axis) components. Determine the angle each force makes with the positive x-axis.
Step 3: Add the horizontal components:
Add all the horizontal components (positive in the rightward direction, negative in the leftward direction) together.
Step 4: Add the vertical components:
Add all the vertical components (positive in the upward direction, negative in the downward direction) together.
Step 5: Use the Pythagorean theorem:
Use the Pythagorean theorem to find the magnitude of the resultant force. The Pythagorean theorem states that the square of the hypotenuse (resultant force) is equal to the sum of the squares of the other two sides (horizontal and vertical components).
Step 6: Find the angle of the resultant force:
Use inverse trigonometric functions to find the angle of the resultant force. The angle can be calculated as the inverse tangent of the vertical component divided by the horizontal component.
By following these steps, you will be able to calculate the resultant of the four given forces.