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Two drivers traveling side-by-side at the same speed suddenly see a deer in the road ahead of them and begin braking. Driver 1 stops by locking up his brakes and screeching to a halt; driver 2 stops by applying her brakes just to the verge of locking, so that the wheels continue to turn until her car comes to a complete stop. (a) All other factors being equal, is the stopping distance of driver 1 greater than, less than, or equal to the stopping distance of driver \(2 ?\) (b) Choose the best explanation from among the following: I. Locking up the brakes gives the greatest possible braking force. II. The same tires on the same road result in the same force of friction. III. Locked-up brakes lead to sliding (kinetic) friction, which is less than rolling (static) friction.

Step by step solution

01

Understanding the Problem

The problem asks us to compare the stopping distances of two drivers braking in different ways: Driver 1 locks up his brakes, causing kinetic friction, while Driver 2 brakes without locking her brakes, maintaining static friction. We need to determine which driver will stop over a shorter distance.

02

Analyze the Types of Friction

We have two types of friction to consider here. Kinetic friction occurs when two surfaces slide against each other, as in the case of a locked brake. Static friction occurs when surfaces are not sliding but may slip, which happens with controlled braking. Importantly, static friction is generally greater than kinetic friction, meaning static friction provides greater braking efficiency.

03

Comparing Stopping Distances

Given that static friction is greater than kinetic friction, driver 2, using static friction, can achieve a greater braking force than driver 1, who uses kinetic friction. As a result, driver 2 will stop in a shorter distance than driver 1, assuming all else is equal.

04

Evaluate the Explanations

Among the explanations I, II, and III, explanations II and III are relevant. II suggests same tires and road results in the same force of friction, which is incorrect due to the nature of friction types. Explanation III correctly states that kinetic friction is less than static friction, leading to a longer stopping distance for kinetic friction (driver 1) compared to static friction (driver 2). Thus, III is the best explanation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kinetic Friction

Kinetic friction is the type of friction that comes into play when two surfaces slide past each other. In our exercise, kinetic friction occurs when driver 1 locks up the brakes, causing the tires to skid across the road. This frictional force is responsible for slowing down the vehicle, but it's less effective compared to static friction.

• When the brakes lock up, the tires lose traction, resulting in skidding.
• Kinetic friction is constant and usually weaker than its counterpart, static friction.
• It depends on the nature of the surfaces in contact and the normal force.

The formula to calculate kinetic friction is given by:\[ f_k = \mu_k \cdot N \]where \( f_k \) is the kinetic friction force, \( \mu_k \) is the coefficient of kinetic friction, and \( N \) is the normal force. Due to its lesser effectiveness, vehicles using kinetic friction for stopping generally require longer stopping distances.

Static Friction

Static friction acts between surfaces that are not sliding past each other. This friction force is present when driver 2 applies brakes in a controlled manner, maintaining the grip between the tire and the road with rotating wheels. Static friction is what helps the car stop smoothly and efficiently.

• Static friction is generally greater than kinetic friction, offering a stronger grip.
• This type of friction prevents slipping, as is the case when the car wheels continue turning while braking.
• It helps in achieving shorter stopping distances.

The formula for static friction is:\[ f_s \leq \mu_s \cdot N \]where \( f_s \) is the static friction force, \( \mu_s \) is the coefficient of static friction, and \( N \) is the normal force applied. In braking scenarios, maintaining static friction is crucial for efficient halting of a vehicle.

Braking Force

Braking force is the force applied by the brakes to slow down or stop a moving vehicle. It is directly influenced by the type of friction acting between the tires and the road. In our exercise, the stopping efficiency depends on whether kinetic or static friction is involved in the braking process.

• Driver 1's braking force is affected by kinetic friction, leading to a longer stopping distance.
• Driver 2 harnesses static friction for a larger braking force, allowing for a shorter stopping distance.

Effectively, the greater the frictional force, the better the braking performance. This is why it is essential to manage braking techniques to avoid skidding and maintain optimal stopping force. The stopping force, therefore, is optimized by keeping the tires rotating under static friction conditions.

Friction Types

Understanding the different friction types is key to analyzing braking and stopping distances. There are several types of friction, but the most relevant for this exercise are kinetic and static friction.

• Kinetic Friction: Occurs when there is sliding motion between surfaces, usually resulting in lower frictional force.
• Static Friction: Acts when there is no relative motion between contact surfaces, offering a robust frictional force.

Static friction is more effective for braking because it offers higher resistance without slipping. In driving, it is preferable to keep the wheels from locking to utilize static friction’s full potential. This understanding helps in making informed decisions about brake application to ensure safety and minimize stopping distances.