Accident at Circular Turn (Skidding)

When a vehicle takes a circular turn, there are several forces at play that can lead to an accident, such as skidding. Skidding occurs when the tires of a vehicle lose their grip on the road surface, causing the vehicle to slide uncontrollably. Understanding the physics behind skidding at a circular turn is crucial for both drivers and engineers to prevent accidents.

Forces in a Circular Turn

When a vehicle is moving in a circular path, it experiences a centripetal force that keeps it moving in a circle. This force is provided by the friction between the tires and the road surface. The maximum frictional force that can be exerted without skidding is given by:

$$ F_{\text{max}} = \mu \cdot N $$

where:

• ( F_{\text{max}} ) is the maximum static frictional force,
• ( \mu ) is the coefficient of static friction between the tires and the road,
• ( N ) is the normal force, which is equal to the weight of the vehicle if the road is flat.

The centripetal force required to keep the vehicle moving in a circle of radius ( r ) at a speed ( v ) is given by:

$$ F_{\text{c}} = \frac{m \cdot v^2}{r} $$

where:

• ( F_{\text{c}} ) is the centripetal force,
• ( m ) is the mass of the vehicle,
• ( v ) is the velocity of the vehicle,
• ( r ) is the radius of the circular turn.

For a vehicle to navigate a turn without skidding, the required centripetal force must be less than or equal to the maximum static frictional force:

$$ \frac{m \cdot v^2}{r} \leq \mu \cdot N $$

Factors Affecting Skidding

Several factors can affect the likelihood of skidding during a circular turn:

• Speed of the Vehicle (v): Higher speeds increase the required centripetal force, making skidding more likely.
• Radius of the Turn (r): A tighter turn (smaller radius) requires more centripetal force, increasing the risk of skidding.
• Coefficient of Friction (μ): Lower friction (e.g., due to wet or icy roads) reduces the maximum static frictional force, making skidding more likely.
• Mass of the Vehicle (m): Heavier vehicles require more centripetal force, which can increase the risk of skidding.
• Tire Conditions: Worn-out tires have reduced friction, increasing the risk of skidding.

Table of Differences and Important Points

Factor	Effect on Skidding Risk	Explanation
Speed (v)	Increases	Higher speed increases the required centripetal force.
Radius of Turn (r)	Increases	Smaller radius increases the required centripetal force.
Coefficient of Friction (μ)	Decreases	Lower friction means less force available to prevent skidding.
Mass (m)	Increases	Heavier vehicles need more force to maintain circular motion.
Tire Conditions	Increases	Worn-out tires reduce the frictional force available to prevent skidding.

Example

Consider a car with a mass of 1000 kg taking a turn with a radius of 50 meters at a speed of 20 m/s. The coefficient of static friction between the tires and the road is 0.7. Will the car skid?

First, calculate the required centripetal force:

$$ F_{\text{c}} = \frac{m \cdot v^2}{r} = \frac{1000 \cdot 20^2}{50} = 8000 \, \text{N} $$

Next, calculate the maximum static frictional force:

$$ F_{\text{max}} = \mu \cdot N = 0.7 \cdot (1000 \cdot 9.8) = 6860 \, \text{N} $$

Since ( F_{\text{c}} > F_{\text{max}} ), the car will skid because the required centripetal force exceeds the maximum static frictional force available.

Conclusion

Understanding the dynamics of skidding at a circular turn is essential for safe driving and road design. By considering the factors that affect skidding, such as speed, turn radius, coefficient of friction, vehicle mass, and tire conditions, drivers can make informed decisions to prevent accidents. Additionally, engineers can design roads and vehicles to minimize the risk of skidding.