Four forces of 10N,8N,6N and 4N act at the same point of an object on bearing 0 degrees,90 degrees,135 degrees and 270 degrees respectively
Fr = 10[0o] + 8[90o] + 6[135o] + 4[270o]=
Resultant force.
X = 10 + 6*Cos135 = 5.76 N.
Y = 8 + 6*sin135 - 4 = 8.24 N.
Tan A = Y/X.
A =
Fr = Y/sinA =
To find the resultant force of the given forces, we need to consider both the magnitude and direction of each force.
Step 1: Break each force into its horizontal and vertical components. We can use trigonometry to find these components.
For the force of 10N at 0 degrees:
Horizontal component = 10N * cos(0 degrees) = 10N * 1 = 10N
Vertical component = 10N * sin(0 degrees) = 10N * 0 = 0N
For the force of 8N at 90 degrees:
Horizontal component = 8N * cos(90 degrees) = 8N * 0 = 0N
Vertical component = 8N * sin(90 degrees) = 8N * 1 = 8N
For the force of 6N at 135 degrees:
Horizontal component = 6N * cos(135 degrees) = 6N * (-0.707) ≈ -4.24N
Vertical component = 6N * sin(135 degrees) = 6N * 0.707 ≈ 4.24N
For the force of 4N at 270 degrees:
Horizontal component = 4N * cos(270 degrees) = 4N * 0 = 0N
Vertical component = 4N * sin(270 degrees) = 4N * (-1) = -4N
Step 2: Add up the horizontal and vertical components of all the forces.
Horizontal component = 10N + 0N + (-4.24N) + 0N = 5.76N (approximately)
Vertical component = 0N + 8N + 4.24N + (-4N) = 8.24N (approximately)
Step 3: Calculate the magnitude and direction of the resultant force using the Pythagorean theorem and trigonometry.
Magnitude of the resultant force = sqrt((horizontal component)^2 + (vertical component)^2)
= sqrt((5.76N)^2 + (8.24N)^2) ≈ 10.02N
Direction of the resultant force = atan(vertical component / horizontal component)
= atan(8.24N / 5.76N) ≈ 56.3 degrees
Therefore, the resultant force has a magnitude of approximately 10.02N and is at a bearing of approximately 56.3 degrees.