Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in Figure 4-46. The sum of the forces A and B exerted on the unit by the horizontal cables is parallel to the line L, and FA = 4300 N. Determine FB and the magnitude of FA + FB.
5600
To determine FB and the magnitude of FA + FB, we can analyze the forces acting on the housing unit.
First, let's understand the forces involved. The two snowcats tow the housing unit using two horizontal cables. FA and FB are the forces exerted on the unit by these horizontal cables.
Since the sum of the forces A and B exerted on the unit by the horizontal cables is parallel to the line L, we can conclude that the force FB is also parallel to the line L.
To determine FB, we need to consider the equilibrium of forces acting on the housing unit. In equilibrium, the sum of the forces acting on an object is equal to zero.
From the given information, we know that FA = 4300 N. Since the sum of the forces in the horizontal direction is zero (due to equilibrium), we can conclude that FB is equal in magnitude but opposite in direction to FA.
Therefore, FB = -4300 N.
To find the magnitude of FA + FB, we simply add the magnitudes of the forces FA and FB, considering the signs:
Magnitude of FA + FB = |FA| + |FB|
= |4300 N| + |-4300 N|
= 4300 N + 4300 N
= 8600 N
So, the magnitude of FA + FB is 8600 N.