Calculate the safe speed with which a train can negotiate a curve of 50 m radius, where the superelevation of the outer rail above the inner rail is 0.6 m. Given that the distance between the rails is 1 m

Explanation

To calculate the safe speed with which a train can negotiate a curve, we can use the formula derived from the principles of circular motion and the geometry of the banked curve.

### Given:
- Radius of the curve (R) = 50 m
- Superelevation (h) = 0.6 m
- Distance between the rails (L) = 1 m
- Acceleration due to gravity (g) = 9.8 m/s²

### Step-by-Step Solution:

1. **Understand the Geometry of the Curve**:
The superelevation (h) is the height difference between the outer rail and the inner rail. The distance between the rails (L) is the horizontal distance.

2. **Use the Formula for Safe Speed**:
The formula to calculate the safe speed (V) for a train negotiating a banked curve is given by:
\[ V = \sqrt{\frac{h \cdot R \cdot g}{L}} \]
where:
- \( h \) = superelevation (height difference)
- \( R \) = radius of the curve
- \( g \) = acceleration due to gravity
- \( L \) = distance between the rails

3. **Substitute the Values**:
Now, substituting the known values into the formula:
\[ V = \sqrt{\frac{0.6 \, \text{m} \cdot 50 \, \text{m} \cdot 9.8 \, \text{m/s}^2}{1 \, \text{m}}} \]

4. **Calculate the Values Inside the Square Root**:
First, calculate the product inside the square root:
\[ 0.6 \cdot 50 \cdot 9.8 = 294 \]
Thus, we have:
\[ V = \sqrt{294} \]

5. **Calculate the Square Root**:
Now, calculate the square root:
\[ V \approx 17.14 \, \text{m/s} \]

### Final Answer:
The safe speed with which the train can negotiate the curve is approximately **17.14 m/s**.

---