A cyclist bends while taking turn to

Options

A. reduce friction
B. generate required centripetal force
C. reduce apparent weight
D. reduce speed

Explanation

To solve the question, "A cyclist bends while taking a turn to:", we need to analyze the forces acting on the cyclist and understand the concept of centripetal force. Here’s a step-by-step solution:

### Step 1: Understand the motion of the cyclist
When a cyclist takes a turn, they are moving along a curved path. This means that the cyclist is undergoing circular motion, which requires a centripetal force to keep them moving in that circle.

**Hint:** Recall that circular motion requires a net inward force directed towards the center of the circle.

### Step 2: Identify the forces acting on the cyclist
In the upright position, the forces acting on the cyclist include:
- Weight (mg) acting downwards.
- Normal force (N) acting perpendicular to the ground.
- Frictional force (f) acting in the direction of motion.

**Hint:** Consider how these forces interact when the cyclist is in a vertical position versus when they bend.

### Step 3: Recognize the need for centripetal force
For the cyclist to successfully navigate the turn, a centripetal force (Fc) is necessary. This force can be expressed as:
\[ Fc = \frac{mv^2}{r} \]
where \( m \) is the mass of the cyclist, \( v \) is the velocity, and \( r \) is the radius of the turn.

**Hint:** Think about what happens if there is insufficient centripetal force while turning.

### Step 4: Analyze the bending action
When the cyclist bends, they change the orientation of the normal force. The bending creates an angle (θ) with the vertical. This angle allows a component of the normal force to act horizontally, which contributes to the centripetal force needed for the turn.

**Hint:** Visualize the triangle formed by the forces when the cyclist bends.

### Step 5: Breakdown of forces when bending
When the cyclist bends at an angle θ:
- The vertical component of the normal force remains \( N \cos(θ) \).
- The horizontal component of the normal force provides the necessary centripetal force \( N \sin(θ) \).

Thus, the centripetal force required for the turn is provided by the horizontal component of the normal force.

**Hint:** Remember that the total force must still balance the gravitational force acting downwards.

### Step 6: Conclusion
The primary reason a cyclist bends while taking a turn is to generate the required centripetal force. By leaning into the turn, the cyclist ensures that a component of the normal force acts towards the center of the circular path, allowing them to navigate the turn safely.

**Final Answer:** A cyclist bends while taking a turn to generate the required centripetal force.