Answer: To find the magnitude and direction of the equilibrant of a system of forces, we first need to find the resultant of the forces, and then find the force that will balance the resultant.
For the given system of forces, we can use the Pythagorean theorem to find the magnitude of the resultant:
R = sqrt(32^2 + 48^2)
= sqrt(1024 + 2304)
= sqrt(3328)
≈ 57.7 N
The direction of the resultant can be found using trigonometry:
tan(theta) = opposite / adjacent
where theta is the angle between the forces, which is 90° in this case. We can choose either force as the adjacent side, and the other force as the opposite side. Let's choose the 32 N force as the adjacent side:
tan(theta) = 48 / 32
theta = atan(48/32)
≈ 56.3°
This means that the resultant has a magnitude of approximately 57.7 N and is directed at an angle of approximately 56.3° to the 32 N force.
To find the equilibrant, we need to find a force that has the same magnitude as the resultant but acts in the opposite direction. We can use the same magnitude and opposite direction to find the equilibrant as:
E = -R
= -57.7 N
This means that the equilibrant has a magnitude of 57.7 N and acts in the opposite direction to the resultant, which is at an angle of approximately 56.3° to the 32 N force.
Explanation: