A force of 6 N and another of 8 N can be applied together to produce the effect of a single force of

Options

A. 1 N
B. 11 N
C. 15 N
D. 20 N

Explanation

To solve the problem of finding the effective single force produced by a 6 N force and an 8 N force, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces**: We have two forces, \( F_1 = 6 \, \text{N} \) and \( F_2 = 8 \, \text{N} \).

2. **Determine Maximum Resultant Force**: The maximum resultant force when both forces are applied in the same direction is given by the sum of the magnitudes of the two forces:
\[ F_{\text{max}} = F_1 + F_2 = 6 \, \text{N} + 8 \, \text{N} = 14 \, \text{N} \]

3. **Determine Minimum Resultant Force**: The minimum resultant force when the two forces are applied in opposite directions is given by the difference of the magnitudes of the two forces:
\[ F_{\text{min}} = |F_2 - F_1| = |8 \, \text{N} - 6 \, \text{N}| = 2 \, \text{N} \]

4. **Establish the Range of Resultant Force**: The resultant force can take any value between the minimum and maximum values calculated:
\[ 2 \, \text{N} \leq F_{\text{resultant}} \leq 14 \, \text{N} \]

5. **Evaluate the Given Options**: The options provided are 1 N, 11 N, 15 N, and 20 N. We need to find which of these values lies within the range of 2 N to 14 N.
- 1 N: Not in the range
- 11 N: In the range
- 15 N: Not in the range
- 20 N: Not in the range

6. **Conclusion**: The only value that lies within the calculated range of 2 N to 14 N is 11 N. Therefore, the effective single force produced by the combination of the two forces is:
\[ \text{Effective Force} = 11 \, \text{N} \]

### Final Answer:
The effective single force produced is **11 N**.