A body is acted upon by two forces of magnitudes 20 N and 30 N. Calculate the maximum and minimum value of resultant force on the body

Answer

To find the maximum and minimum values of the resultant force when two forces are acting on a body, we can use the following principles from vector addition.

### Step-by-Step Solution:

1. **Identify the Forces**:
We have two forces acting on the body:
- Force \( F_1 = 20 \, \text{N} \)
- Force \( F_2 = 30 \, \text{N} \)

2. **Understanding Resultant Force**:
The resultant force \( R \) when two forces are acting at an angle can be calculated using the formula:
\[ R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos \theta} \]
where \( \theta \) is the angle between the two forces.

3. **Maximum Resultant Force**:
The maximum resultant force occurs when the two forces are acting in the same direction (i.e., \( \theta = 0^\circ \)). In this case:
\[ R_{\text{max}} = F_1 + F_2 = 20 \, \text{N} + 30 \, \text{N} = 50 \, \text{N} \]

4. **Minimum Resultant Force**:
The minimum resultant force occurs when the two forces are acting in opposite directions (i.e., \( \theta = 180^\circ \)). In this case:
\[ R_{\text{min}} = |F_1 - F_2| = |20 \, \text{N} - 30 \, \text{N}| = 10 \, \text{N} \]

5. **Final Result**:
Therefore, the maximum and minimum values of the resultant force on the body are:
- Maximum Resultant Force \( R_{\text{max}} = 50 \, \text{N} \)
- Minimum Resultant Force \( R_{\text{min}} = 10 \, \text{N} \)

### Summary:
- Maximum Resultant Force: \( 50 \, \text{N} \)
- Minimum Resultant Force: \( 10 \, \text{N} \)