Car Braking and Sliding Explained

When a car is moving, friction between the tires and the road allows it to accelerate, decelerate, and turn. This friction opposes the motion or the tendency of motion between the tire surface and the road surface.

When you apply the brakes, the braking system applies a torque to the wheels. This braking torque slows down or stops the rotation of the wheels. As the wheels slow down, the tire's contact patch attempts to move relative to the road surface. Static friction acts to oppose this relative motion, allowing the car to decelerate without sliding.

Friction and Sliding Conditions

The road provides a maximum static friction force that can be exerted on the tire before it starts to slide. This maximum force is called the limiting friction force. As long as the force required to slow down the car (which is related to the applied braking torque) is less than or equal to this limiting friction force, the tires will roll without sliding.

However, if the force required to slow down the car exceeds the maximum static friction force available, the tires will lose their grip on the road, and the car will begin to slide. This happens when the wheels lock up (stop rotating) or slow down so much that the tire surface starts skidding over the road surface.

Relating Braking Torque to Sliding

The braking torque applied to the wheels creates a braking force at the contact patch between the tire and the road. This braking force is what tries to stop the car. The car will continue to decelerate without sliding as long as the braking force requested by the braking torque is balanced by the static friction force from the road.

Sliding occurs when the braking system tries to apply a braking force (derived from the braking torque) that is greater than the maximum possible static friction force the road can provide. In simple terms, the braking torque is too high, demanding a stopping force that the friction cannot supply, leading to the tires skidding.

Analyzing the Options

• The question asks when the car will begin to slide.
• Sliding happens when the force attempting to cause relative motion (related to braking torque) overcomes the static friction force.
• The limiting friction force is the maximum static friction force.
• Therefore, sliding begins when the effect of the braking torque (the braking force it tries to generate) is greater than the limiting friction force.

Looking at the options:

• Option 1:

  Braking torque is higher than limiting friction force from the road

  - This aligns with our understanding that sliding happens when the braking effort exceeds the maximum available friction.
• Option 2:

  Braking torque is equal to limiting friction force from the road

  - At this point, sliding is just about to begin, or the wheels are rolling at the edge of slipping, but not necessarily sliding yet. Sliding *begins* when it is *higher*.
• Option 3:

  Braking torque is less than limiting friction force from the road

  - In this case, the friction force is sufficient to stop the wheel from sliding, so the car will decelerate without sliding.
• Option 4:

  They don’t have any relation

  - This is incorrect; braking torque and friction are directly related to a car's ability to brake and whether it slides.

Based on this analysis, the car will begin to slide when the braking torque is high enough to demand a braking force greater than the limiting friction force the road can provide.