Knowing that the coefficient of static friction between the...

Knowing that the coefficient of static friction between the tires and the road is 0.80 for the automobile shown, determine the maximum possible acceleration on a level road, assuming ( $a$ ) four-wheel drive, (b) rear-wheel drive, $(c)$ front-wheel drive.

Key Concepts

Coefficient of Static Friction

This is a measure of how much grip exists between two surfaces—in this case, between the tires and the road. It represents the ratio of the maximum static frictional force that can be exerted without slipping over the normal force. A higher coefficient indicates better adhesion, which directly influences the maximum force that can be used to accelerate the vehicle without tire slip.

Newton's Second Law

Newton’s Second Law of Motion, which states that the net force acting on an object is equal to its mass times its acceleration, is fundamental in determining the maximum acceleration of a vehicle. In this context, the frictional force provided by the tires is the net force that accelerates the car, and this law allows us to relate the frictional force to the acceleration.

Traction Force

Traction force is the maximum force that the tires can exert on the road before slipping occurs. It is determined by multiplying the coefficient of static friction by the normal force (which, for a level road, is equivalent to the weight distribution). This limit defines the maximum possible acceleration that can be achieved without losing grip.

Drive Wheel Configuration

The drive wheel configuration—whether a vehicle is four-wheel drive, rear-wheel drive, or front-wheel drive—affects how the available traction force is distributed across the tires. In a four-wheel drive system, all wheels contribute to acceleration, maximizing the use of available friction. In contrast, for rear- or front-wheel drive, only half of the tires are responsible for applying the traction force, typically resulting in a lower maximum acceleration capability.

Transcript

00:01 Okay, for this problem we are solving the maximum acceleration of a vehicle on a flat road in three different instances the first instance four -wheel drive the second instance rear -wheel drive and the third instance front wheel drive so right here we're starting off with four -wheel drive.

00:19 We want to sum the forces in the wide direction we have two normal forces that offset the weight of the car and now summing the forces in the x direction we have two frictional forces that offset the acceleration and substituting the coefficient of static friction in there and reducing the mass will give us the acceleration in terms of gravity and the coefficient of static friction and if we plug those numbers in right here we get 25 .76 feet per second squared and i need to box that in so that was the solution to the first part of the problem now for rear wheel drive, we want to take the sum of the moments about the front wheel.

01:24 And we'll assume counterclockwise rotation is positive.

01:28 So we have the weight minus the normal force and rewriting this in terms of that normal force and reducing.

01:48 Now if we multiply by the coefficient of static friction, we have this in terms of the frictional force.

01:56 Now we're going to use that whenever we sum the forces in the x direction, which in this instance is just the friction on the back tire and the mass times acceleration.

02:14 And if we write this with the first equation substituted into it, and we can reduce the equation by canceling out the mass from everything.

02:39 Now if we combine like terms, we have that right there...

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