Final answer:
Based on the vector addition of the given forces, none of the provided options for Fc and Fb match the calculations obtained from the sum of the components in each direction, suggesting an error in the options or calculation.
Step-by-step explanation:
The question asks for the values of forces Fc and Fb given that the net forces in the x and y directions add up to zero. To find these, we need to use the principle of superposition of forces, which states that forces can be added vectorially to get the resultant force. Since all forces add up to zero, vector addition reveals that the sum of their components in each direction must also equal zero.
The x-components of the given forces are -34.6, -36, and 40. Adding them together:
-34.6 - 36 + 40 + Fc_x = 0
This simplifies to Fc_x = 30.6 lb.
The y-components of the given forces are 20, -48, and 30. Adding them together:
20 - 48 + 30 + Fb_y = 0
This simplifies to Fb_y = -2 lb.
However, with the information given and the options provided, none of the choices for Fc and Fb match the calculated values. So, it seems that there might be an error, either in the calculation or the provided options. Provided that the components given are correct, and assuming no other forces are involved, the values indicated for Fc and Fb would not cause the system to be in equilibrium.