A body is in equilibrium under the action of 3 force.one is 6Ndue east and the other is 3Nacting in a direction 60'north
the "balancing" 3rd force is the force 180º opposite the vector addition of the given forces
All angles are measured CCW from +x-axis.
F1 + F2 = 6[0o] + 3[60o]. = 6 + 1.5+2.6i = 7.5 + 2.6i = 7.94N[19o].
F3 = 7.94[19o+180o] = 7.94N[199o].
To determine whether a body is in equilibrium under the action of multiple forces, we need to analyze the vector sum of all the forces acting on the body. If the vector sum of the forces is zero, then the body is in equilibrium.
In this case, we have two forces acting on the body: 6N due east and 3N acting at a direction 60° north.
To find the vector sum of these forces, we can break each force into its horizontal (x-direction) and vertical (y-direction) components.
The force of 6N due east can be broken into 6N in the x-direction (east) and 0N in the y-direction.
The force of 3N acting at a direction 60° north can be broken into 3N multiplied by the sin(60°) in the y-direction and 3N multiplied by cos(60°) in the x-direction.
Thus, the force of 3N acting at a direction 60° north can be broken down into 3N * sin(60°) in the y-direction and 3N * cos(60°) in the x-direction.
Now, add up the x-direction components and the y-direction components separately to get the resulting force in each direction.
For the x-direction:
6N (from the force due east) + 3N * cos(60°) (from the force at 60° north) = 6N + 3N * 0.5 = 6N + 1.5N = 7.5N in the x-direction.
For the y-direction:
0N (from the force due east) + 3N * sin(60°) (from the force at 60° north) = 0N + 3N * 0.87 (approximately) = 0N + 2.61N = 2.61N in the y-direction.
Now we have the x-component as 7.5N and the y-component as 2.61N. To find the resultant force, we can use the Pythagorean theorem:
√(7.5N^2 + 2.61N^2) = √(56.25N^2 + 6.8121N^2) = √63.0621N^2 = 7.949N (approximately)
The magnitude of the resultant force is approximately 7.949N. Since the vector sum of the forces is not zero, the body is not in equilibrium.
Additionally, to fully describe the equilibrium of the body, we also need to consider the direction of the resultant force. We can find this by using the inverse tangent function:
tan^(-1)(2.61N/7.5N) ≈ 19.03°
The direction of the resultant force is approximately 19.03° above the x-axis (east).