With aid of diagram find the resultant and equilibriant of two forces, 10N acting in the direction of North 30 East and 15N acting in the easterly direction, if both forces act at a point.
To find the resultant and equilibrant of two forces, we can use the graphical method known as the parallelogram law of forces. This method involves constructing a parallelogram using the two given forces as adjacent sides.
Here's a step-by-step guide on finding the resultant and equilibrant using a diagram:
Step 1: Draw a horizontal line to represent the direction of East and label it as "→" (positive x-axis direction). Then, draw a vertical line perpendicular to the horizontal line to represent the direction of North. Label this line as "↑" (positive y-axis direction).
Step 2: Starting from the point of action, draw a line in the direction of North 30 degrees East. This line should make a 30-degree angle with the positive x-axis. Label this line as "Force A" and write the magnitude of the force, which is 10N.
Step 3: Starting from the same point of action, draw a line in the easterly direction. This line should be parallel to the positive x-axis. Label this line as "Force B" and write the magnitude of the force, which is 15N.
Step 4: Complete the parallelogram by drawing lines parallel to the two given forces. These lines should connect the endpoints of the forces. Label the diagonal line as "Resultant" and mark its magnitude using a ruler.
Step 5: To find the equilibrant, draw a line from the same point of action in the opposite direction of the resultant. This line should be parallel to the resultant line, pointing towards the opposite side of the parallelogram. Label this line as "Equilibrant" and mark its magnitude.
Step 6: Measure the magnitude of the resultant and equilibrant using a ruler, and write down their values.
Using this graphical method, you can find the magnitude and direction of the resultant and equilibrant forces.