Question

A cyclist bends while taking turn in order to

• A. reduce friction
• B. provide required centripetal force
• C. reduce apparent weight
• D. reduce speed
• E. sit comfortably

Hint:

The angle of bending is given by $\tan\theta = \frac{v^2}{rg}$. Higher speeds or sharper turns require the cyclist to lean further inward 40].

Answer 1

The Correct Option is B

Concept: When a cyclist moves along a curved path, they are in a state of rotational motion which requires an inward force (centripetal force) directed toward the center of the curve.
• Centripetal Force: $F = \frac{mv^2}{r}$.
• Forces Acting: Weight ($mg$) acts downward, and the normal reaction ($R$) acts from the ground.

Step 1: Analyze the mechanics of bending.
By bending inward at an angle $\theta$ with the vertical, the cyclist causes the normal reaction force from the ground to tilt. This tilted reaction force can be resolved into a vertical component that balances the weight and a horizontal component directed toward the center.

Step 2: Identify the role of the horizontal component.
The horizontal component of the normal reaction provides the necessary centripetal force required to maintain the circular path. Without this bending, the cyclist would rely solely on friction, which might be insufficient, leading to skidding.