the snowcats in Antarctica are towing a housing unit North, as show in fig. 4-50. The sum of the forces FA and FB exerted on the unit by the horizontal cables in North, parallel to the line L, and FA = 4500 N. Determine FB and the magnitude of FA + FB. explain in detail with example
To determine FB, we need to consider the horizontal equilibrium of the housing unit. Since it is being towed North and there are no other forces acting horizontally, the sum of the horizontal forces must be zero.
Let's consider FA as a positive force and FB as a negative force (opposite direction to FA). Since the sum of the forces must be zero, we can write the equation:
FA + FB = 0
Substituting the given value for FA:
4500 N + FB = 0
To solve for FB, we need to isolate it on one side of the equation. Subtracting 4500 N from both sides:
FB = -4500 N
Therefore, FB is -4500 N, which means it is acting in the opposite direction (South) to FA.
To find the magnitude of FA + FB, we simply add the magnitudes (ignoring the directions):
Magnitude of FA + FB = |FA| + |FB|
Since both FA and FB have the same magnitude (4500 N), we can write:
Magnitude of FA + FB = 4500 N + 4500 N = 9000 N
Therefore, the magnitude of FA + FB is 9000 N.
In summary, FB is -4500 N (acting South) and the magnitude of FA + FB is 9000 N (ignoring the directions).