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Equilibrium occurs when the net force acting on an object is zero, meaning all forces balance each other out. According to Newton's First Law of Motion, an object at rest remains at rest, and an object in motion remains in motion at a constant velocity unless acted upon by an unbalanced force. In the given problem, the object continues to move at a constant velocity, which indicates that the forces acting on it are in equilibrium.

Think of equilibrium like a tug-of-war game, where both sides pull with equal strength. If neither side moves, the system is balanced or in equilibrium. For the moving object, even though it's in motion, the forces applied to it are perfectly balanced along the north, west, south, and east directions, resulting in a zero net force. Understanding equilibrium is essential when dealing with motion, as it helps us identify scenarios where forces are balanced, thus allowing the object to maintain constant velocity.

Vector addition is a mathematical way to combine forces that have both magnitude (strength) and direction (way they are pointing). In this exercise, we have two vectors: one pointing north with 80.0 N and another pointing west with 60.0 N. These vectors tell us exactly how much force is acting in specific directions.

When adding vectors, think about walking in a straight line: first go north, then west. You don't walk diagonally unless the directions are combined. Vector addition uses these directions to form a triangle, with the third side representing the resultant vector, which is the combination of both forces. Using vector addition allows us to find the single vector that can replace multiple vectors and will produce the same effect on an object.

• Use the tip-to-tail method to combine vectors.
• The resultant vector (or net force) in equilibrium should sum to zero.
• Both the size and direction of each vector matter.

To maintain an object's constant movement, understanding force magnitude and direction is crucial. The magnitude of a force is its strength, while its direction indicates the way it pushes or pulls the object. For the third force in our problem, its magnitude was calculated using Pythagoras’ theorem, as it's the diagonal of the right triangle formed by the north and west forces.

The calculations show that the third force must have a magnitude of 100.0 N. Its direction is determined by resolving the angle using the tangent function, giving an angle 53.1 degrees south of east.

• The magnitude is found using the formula \( \text{Magnitude} = \sqrt{(\text{north force})^2 + (\text{west force})^2} \).
• The direction involves finding the angle, \( \theta \), using \( \tan(\theta) = \frac{\text{opposite component}}{\text{adjacent component}} \).
• A proper understanding of both magnitude and direction helps predict how and where an object will move.