Static friction coefficient question

[hamsterpower7]

Homework Statement

from giancoli 5th ed (algebra based)
chapter 4, question 42


Drag race tires in contact with an asphalt surface probably have one of the higher coefficients of static friction in the everyday world. Assuming a constant acceleration and no slipping of tires estimate the coefficient of static friction for a drag racer that covers the quarter mile in 6.0s

Homework Equations

The Attempt at a Solution

I converted quarter mile to m ----> 402.5m

using kinematic formula i found the acceleration a=22.36 m/s^2

$$\Sigma F = F_A - F_fr$$

$$F_A - \mu_s F_N = mass 22.36 m/s^2$$

and than I got stuck...
the answer key states that I shouldn't have put applied force in the equation
but how does that make sense? the person should have put applied for to have constant acceleration

anyways if there wasn't a applied force I can solve for static friction from the equation above

help me please

 

[obafgkmrns]

Keep in mind that the friction force (coefficient of friction times mass of car times acceleration of gravity) will be equal to the applied force (mass of car times its acceleration) if you assume that the car is accelerating as fast as it can without losing traction.

 

[hamsterpower7]

Keep in mind that the friction force (coefficient of friction times mass of car times acceleration of gravity) will be equal to the applied force (mass of car times its acceleration) if you assume that the car is accelerating as fast as it can without losing traction.

I don't get this, isn't applied force and friction force two separate force?

 

[obafgkmrns]

In this case, they are one and the same! The car's tire is exerting a friction force parallel to the ground that accelerates the car. That friction force can be no greater than the tire's normal force times the coefficient of friction.

 

[rwisz]

Hello,

Thank you for your question. I can understand why you may be confused about the concept of static friction and the lack of an applied force in the equation provided. Let me try to explain it in a bit more detail.

First, let's define the coefficient of static friction as the ratio of the maximum static friction force to the normal force between two surfaces. In this case, the surfaces are the drag racer's tires and the asphalt surface. The coefficient of static friction is dependent on the materials of the two surfaces and is a measure of how well they "stick" together.

Now, in order for there to be static friction, there must be a force acting on the tires that is trying to make them slip on the ground. This force is known as the applied force or the driving force. In the case of a drag racer, this would be the force from the engine that propels the car forward. However, in this question, we are assuming that the acceleration is constant and there is no slipping of the tires. This means that the applied force is equal to the maximum static friction force, and this is why it does not need to be included in the equation.

So, to solve for the coefficient of static friction, we can use the equation you provided:

\Sigma F = F_A - F_fr

Since we know that the acceleration is constant and there is no slipping, we can rewrite this equation as:

\Sigma F = ma - F_fr

And since we are looking for the coefficient of static friction, we can rearrange this equation to solve for it:

\mu_s = \frac{ma - F_fr}{F_N}

Now, we know that the mass is given, and we can calculate the normal force using the weight of the car (mass x gravity). The only unknown in this equation is the maximum static friction force, which we can calculate using the acceleration and the mass of the car. Once we have all the values, we can solve for the coefficient of static friction.

I hope this explanation helps to clarify the concept for you. If you have any further questions, please don't hesitate to ask.