ABCDE is a pentagon. Forces AB,AE,DC and ED act at a point. Which force should be added to this systemm to make the resultant 2AC?

Options

A. AC
B. AD
C. BC
D. BD

Explanation

To solve the problem step by step, we will analyze the forces acting on the pentagon ABCDE and determine which additional force is needed to achieve a resultant force of 2AC.

### Step-by-step Solution:

1. **Identify the Forces**:
The forces acting at point A are AB, AE, DC, and ED. We need to find an additional force that, when added to these, results in a force of 2AC.

2. **Draw the Pentagon**:
Visualize or sketch the pentagon ABCDE. Label the points A, B, C, D, and E. This will help in understanding the directions of the forces.

3. **Understand Vector Addition**:
Recall that forces are vectors, and their resultant can be found using vector addition. The resultant of two vectors can be found by placing them head to tail.

4. **Combine Forces**:
Notice that the forces ED and DC can be combined:
- The resultant of vector ED and vector DC is vector EC (from E to C).
- This can be written as:
\[ \vec{ED} + \vec{DC} = \vec{EC} \]

5. **Combine with AE**:
Now, consider the force AE along with the resultant EC:
- The resultant of vector AE and vector EC is vector AC (from A to C).
- This can be expressed as:
\[ \vec{AE} + \vec{EC} = \vec{AC} \]

6. **Express AC in Terms of Given Forces**:
Substitute EC with the expression from step 4:
\[ \vec{AE} + (\vec{ED} + \vec{DC}) = \vec{AC} \]
This simplifies to:
\[ \vec{AE} + \vec{ED} + \vec{DC} = \vec{AC} \]

7. **Add Remaining Force AB**:
Now, we need to consider the force AB:
- If we add AB to the left side of the equation, we have:
\[ \vec{AB} + \vec{AE} + \vec{ED} + \vec{DC} = \vec{AC} + \vec{AC} \]
Which simplifies to:
\[ \vec{AB} + \vec{AE} + \vec{ED} + \vec{DC} = 2\vec{AC} \]

8. **Conclusion**:
From the equation derived, we can see that the additional force needed to achieve a resultant of 2AC is the force DC. Therefore, the answer is:
- **Force DC should be added to the system**.