A AND B HAS DIFFERENT VALUES OF LIFTING POINTS, SHOW THE CALCULATIONS FOR ALL POINTS BASED ON THE GIVEN DIMENSIONS VALUE

Let's proceed with the calculations by considering that each point (A, B, C, D, E, F) may have different lifting forces. The steps involved will include calculating the moments about a point and then solving the system of equations.

### Step 1: Assign Coordinates to Each Point
We'll assume a coordinate system with point A as the origin (0,0):

- **Point A (0, 0)**
- **Point B (27.52, 0)**
- **Point C (73.01, 0)**
- **Point D (0, 26.89)**
- **Point E (27.52, 26.89)**
- **Point F (73.01, 26.89)**

The Center of Gravity (CG) is located at:
- **CG (47.96, 10.13)**

### Step 2: Equilibrium Conditions
We have two main conditions to satisfy:
1. **Vertical force equilibrium:**
   \[
   F_A + F_B + F_C + F_D + F_E + F_F = 100 \text{ lbs}
   \]
   
2. **Moment equilibrium around point A:**
   \[
   \text{Sum of moments around A} = 0
   \]
   
   The moment around point A is calculated as:
   \[
   F_B \cdot 27.52 + F_C \cdot 73.01 + F_D \cdot 0 + F_E \cdot 27.52 + F_F \cdot 73.01 = 100 \cdot 47.96
   \]

### Step 3: Calculation of Moments
We can now set up the moment equation:

\[
27.52 \cdot F_B + 73.01 \cdot F_C + 0 \cdot F_D + 27.52 \cdot F_E + 73.01 \cdot F_F = 100 \cdot 47.96
\]
\[
27.52 \cdot F_B + 27.52 \cdot F_E + 73.01 \cdot (F_C + F_F) = 4796 \text{ lbs-in}
\]

### Step 4: Additional Equilibrium Considerations
Since the system has vertical forces, we'll consider equilibrium in the y-direction as well:
\[
F_A + F_B + F_C + F_D + F_E + F_F = 100 \text{ lbs}
\]

### Step 5: Solve the Equations
We can now solve the equations simultaneously. Let's do that.

1. **Vertical force equilibrium:**
   \[
   F_A + F_B + F_C + F_D + F_E + F_F = 100 \text{ lbs}
   \]

2. **Moment around A:**
   \[
   27.52 \cdot F_B + 73.01 \cdot F_C + 27.52 \cdot F_E + 73.01 \cdot F_F = 4796 \text{ lbs-in}
   \]

We can substitute the values into a system of linear equations and solve for the forces \( F_A, F_B, F_C, F_D, F_E, F_F \).

### Step 6: Calculation and Solving the System

Let me calculate the values for each force.The calculations resulted in the following relationships between the forces at each lifting point:

1. **Force at Point B** (\(F_B\)):
   \[
   F_B = -1.605 \times F_A - 1.605 \times F_D - F_E + 55.067
   \]

2. **Force at Point C** (\(F_C\)):
   \[
   F_C = 0.605 \times F_A + 0.605 \times F_D - F_F + 44.933
   \]

These expressions indicate how forces \( F_B \) and \( F_C \) depend on the forces at points A, D, E, and F. These relationships need to be satisfied to ensure that the sum of forces equals the total weight (100 lbs) and that the moments about point A balance.

### Next Steps:
To find the exact values for each force (\( F_A, F_B, F_C, F_D, F_E, F_F \)), you would need additional information or assumptions. For example, if you assume that points A and D carry equal loads, and similarly for points B and E, and C and F, then you can solve for the exact force values.

Would you like to proceed with specific assumptions or provide additional information to continue the calculations?

Explore detailed calculations for different lifting points (A, B, C, D, E, F) in mechanics, considering varying lifting forces and given dimensions. Understand how to apply equilibrium conditions and moment equations to solve for each force. Suitable for advanced high school students and engineering enthusiasts.

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