The breadth of an iron door is 2.4 m. If the minimum torque required to open the door is 50 Nm, what is the minimum force required to open the door?

Answer

To find the minimum force required to open the door, we can use the formula for torque:

### Step-by-Step Solution:

1. **Understand the Formula for Torque**:
Torque (τ) is defined as the product of the force (F) applied and the perpendicular distance (R) from the pivot point to the line of action of the force. The formula is:
\[ \tau = F \times R \]

2. **Identify the Given Values**:
From the problem, we know:
- Torque (τ) = 50 Nm
- Perpendicular distance (R) = 2.4 m

3. **Rearrange the Formula to Solve for Force**:
We need to find the force (F), so we rearrange the formula:
\[ F = \frac{\tau}{R} \]

4. **Substitute the Known Values into the Formula**:
Now we can substitute the values we have into the rearranged formula:
\[ F = \frac{50 \, \text{Nm}}{2.4 \, \text{m}} \]

5. **Perform the Calculation**:
Now, we perform the division:
\[ F = \frac{50}{2.4} \approx 20.833 \, \text{N} \]

6. **Conclusion**:
Therefore, the minimum force required to open the door is approximately:
\[ F \approx 20.833 \, \text{N} \]

### Final Answer:
The minimum force required to open the door is **20.833 Newtons**.

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