(II) Two large snowcats are towing a housing unit north, as shown in Fig. 4–42. The sum of the forces F_A and F_B exerted on the unit by the horizontal cables is north, parallel to the line L, and F_A = 4200 N. Determine F_B and the magnitude of F→_A + F→_B . <IMAGE>

Verified step by step guidance

1. Identify the direction and magnitude of the forces involved. Here, F_A is given as 4200 N directed north. Assume F_B also acts along the same line but the exact direction and magnitude are unknown.
2. Since the resultant force F→_A + F→_B is directed north and parallel to line L, use vector addition to find F_B. Represent F_A and F_B as vectors along the north direction.
3. Set up the equation for vector addition of F_A and F_B to equal the resultant force vector F→_A + F→_B. This can be expressed as F_A + F_B = F→_A + F→_B.
4. Solve for F_B by rearranging the vector addition equation. If additional information about the angle or the resultant force magnitude is given, use it to find F_B.
5. Calculate the magnitude of the resultant force vector F→_A + F→_B using the Pythagorean theorem if the forces are not collinear, or by simple addition if they are collinear.

Key Concepts

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law can be expressed with the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. In the context of the question, understanding this law is crucial for analyzing the forces acting on the housing unit being towed.

Vector Addition

Vector addition involves combining two or more vectors to determine a resultant vector. In this scenario, the forces F_A and F_B are vectors that need to be added to find the total force acting on the housing unit. The direction and magnitude of each force must be considered, as they can affect the overall motion of the unit.

Equilibrium of Forces

An object is in equilibrium when the sum of all forces acting on it is zero, resulting in no acceleration. In this problem, if the housing unit is being towed at a constant velocity, the forces F_A and F_B must balance out any opposing forces, such as friction. Understanding equilibrium helps in determining the relationship between the forces and calculating the unknown force F_B.