Determine graphically the equilibrant of two forces of 15N and 20N if the angle between them is 135degrees
F1 = 15N[0o], F2 = 20N[135o].
F1+F2 = 15 + -14.1+14.1i = 0.9 + 14.1i = 14.2 N.[86.4o] = 0.89 + 14.18i
F3 must be equal to F1+F2 in magnitude and 180o out of phase:
F3 = 14.2N[86.4+180] = 14.2[266.4o].= 14.2[86.4o] S. of W. = -0.89 - 14.18i
To determine the equilibrant of two forces graphically, follow these steps:
Step 1: Draw a diagram
Draw a vector diagram to represent the forces. Start by drawing a horizontal line to represent the x-axis and a vertical line to represent the y-axis. Label one end of these lines as the origin.
Step 2: Represent the forces
Draw one force vector with a magnitude of 15N at any desired angle relative to the x-axis. Then, draw another force vector with a magnitude of 20N in the same manner. Make sure to label the magnitudes of the forces.
Step 3: Determine the resultant vector
Using the head-to-tail method, draw a vector from the tail of the first vector to the head of the second vector. This resultant vector represents the sum of the two forces.
Step 4: Draw the equilibrant
To draw the equilibrant, reverse the direction of the resultant vector by drawing a vector from the head of the resultant vector to its tail.
Step 5: Measure the magnitude and angle
Measure the magnitude of the equilibrant using a ruler. In this case, the magnitude of the equilibrant is likely to be less than the magnitudes of the two forces since the forces are not balanced. Also, use a protractor to measure the angle between the equilibrant and the x-axis.
By following these steps, you can graphically determine the equilibrant of two forces.
Note: If you prefer to solve it mathematically using equations, you can use the law of cosines and the law of sines to calculate the magnitude and angle of the equilibrant.