Question

Leonardo da Vinci discovered that the magnitude of the friction force is usuzlly simply proportional to the magnitude of the normal force; that is, the friction force does not depend on the width or length of the contact area. Thus, the main reason to use wide tires on a race car is that they a) Iook cool. b) have more apparent contact area. c) cost more. d) can be made of softer materials.

Short answer

Answer: Wide tires are used on a race car because they can be made of softer materials, which can improve grip and control.

Step-by-step solution

Understanding the relationship between friction force and normal force

According to Leonardo da Vinci's discovery, the friction force is proportional to the normal force. This means that if the normal force increases, the friction force will also increase. The friction force does not depend on the width or length of the contact area.

Analyzing the given options

Now, let's analyze each option to see which one is the most suitable: a) Iook cool: This is not a scientific reason to use wide tires in race cars. b) have more apparent contact area: As mentioned earlier, the friction force does not depend on the width or length of the contact area. So, this option is also not valid. c) cost more: The cost does not have any direct relation to the friction force and normal force. This option is not applicable as well. d) can be made of softer materials: The use of softer materials can increase the friction between the tire and the surface, which can help to improve the grip and control of the race car. Thus, this option seems to have a logical explanation for using wide tires in a race car.

Final answer

Based on our analysis, the correct choice is (d) can be made of softer materials, which can improve grip and control in a race car.

Key concepts

Normal Force

Normal force is an essential concept in understanding friction, especially in automotive contexts. It is the force that a surface exerts to support the weight of an object resting on it. This force acts perpendicular to the surface. In the case of race cars, the normal force is crucial as it influences the frictional force.

The normal force can be affected by several factors, including:

• The weight of the vehicle: Heavier vehicles tend to exert a larger normal force.
• Inclination of the surface: On a slope, the normal force is reduced as part of the weight is directed parallel to the incline.

Since Leonardo da Vinci observed that friction was proportional to the normal force, increasing the normal force leads to higher friction. This relationship is depicted by the equation:\[ F_{ ext{friction}} = u imes F_{ ext{normal}} \]where \( F_{ ext{friction}} \) is the force of friction, \( u \) is the coefficient of friction, and \( F_{ ext{normal}} \) is the normal force.

In race cars, leveraging the normal force can significantly impact performance, especially during high-speed maneuvers.

Contact Area

Contact area refers to the region where two surfaces touch each other. In the context of tires, it is the part of the tire that physically contacts the road surface at any given time. Although it might appear that a larger contact area would result in increased friction, da Vinci's observations tell us otherwise.

Interestingly, the friction force does not depend on the size of the contact area. Instead, it's about the interaction between materials and the normal force. Here’s why the contact area can still play a subtle role:

• A larger contact area can distribute heat better, which is critical during races to prevent tire overheating.
• It can provide additional surface to manage tire wear uniformly.

Thus, while the contact area doesn't directly influence friction, it impacts other dynamics like tire durability and performance consistency.

Race Car Tires

Race car tires are engineered with one primary goal: to maximize grip. These tires are not just about looks or costs; their design serves a functional role. A significant aspect that sets them apart is the material composition, often allowing for softer compounds.

Softer materials increase the friction between the tire and the track, ensuring better traction. This enhanced grip assists in achieving faster acceleration, sharper turns, and more effective braking. However, softer tires also wear down quicker, which is a trade-off teams strategically manage.

Moreover, the increased width of race car tires provides benefits beyond what might seem apparent. While not contributing directly to friction via increased contact area, wider tires can handle higher loads, improving vehicle stability and responsiveness. Such features are pivotal under the intense demands of competitive racing conditions. Therefore, design choices in race car tires reflect a balance between maximizing performance and managing wear.