A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it

Options

A. increase
B. decrease
C. remains the same
D. fluctuates

Answer

To solve the problem regarding the normal force acting on a motorcycle ascending an overbridge of radius \( R \) while maintaining a constant speed, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Forces Acting on the Motorcycle:**
- When the motorcycle is on the overbridge, two main forces act on it: the gravitational force (\( mg \)) acting downward and the normal force (\( N \)) acting perpendicular to the surface of the bridge.

2. **Identifying the Components of Forces:**
- As the motorcycle ascends, we can break down the gravitational force into two components:
- One component acting towards the center of the circular path: \( mg \cos \theta \)
- The other component acting perpendicular to the surface: \( mg \sin \theta \)

3. **Applying Newton's Second Law:**
- For circular motion, the net centripetal force required to keep the motorcycle moving in a circle is given by:
\[ F_{\text{centripetal}} = \frac{mv^2}{R} \]
- The net force towards the center of the circle can be expressed as:
\[ mg \cos \theta - N = \frac{mv^2}{R} \]
- Rearranging this gives us the equation for the normal force:
\[ N = mg \cos \theta - \frac{mv^2}{R} \]

4. **Analyzing the Change in Normal Force:**
- As the motorcycle ascends the overbridge, the angle \( \theta \) decreases. This means that \( \cos \theta \) increases because cosine is a decreasing function in the range of \( 0 \) to \( 90 \) degrees.
- Since the speed \( v \) is constant, the term \( \frac{mv^2}{R} \) remains constant.

5. **Conclusion on Normal Force:**
- As \( \cos \theta \) increases, the term \( mg \cos \theta \) increases, leading to an increase in the normal force \( N \).
- Therefore, the normal force acting on the motorcycle **increases** as it ascends the overbridge.

### Final Answer:
The normal force on the motorcycle **increases** as it ascends the overbridge.

---