How Does Static Friction Determine Car Braking Acceleration?

[scavok]

The coefficient of static friction between the tires of a car and a horizontal road is s=0.56. If the net force on the car is the force of static friction exerted by the road, what is the magnitude of the maximum acceleration of the car when it is braked?

I really don't understand what is going on in this question. How can I solve this without the mass, velocity, or acceleration of the car? Why is it talking about static friction instead of kinetic friction if the car is moving? How can the net force be the static friction exerted by the road if the car is moving?

vvv Thanks, that's what I needed.

 

[andrevdh]

When the tyres of a car are rolling over the road surface there are no relative motion between the contact point of the tyre and the road - only static friction acts on the tyre. If the car is turning the wheels this friction acts towards the front on the tyres thus pushing the car forwards (action-reaction pairs). When the car is braking this frictional force will act towards the rear of the car, thus slowing it down. As long as the car is not skidding we will be dealing with static friction for the braking force on the car. Static friction can increase only up to a certain limit, so this condition will only do so much before the tyres start to slip over the road when applying the brakes too hard, in which case we are dealing with kinetic friction - which is generally smaller than static friction anyway, unless the rubber starts to melt!

 

[kyle8921]

Hi there,

Thank you for your question. I understand your confusion and I will try to provide an explanation for you.

Firstly, static friction and kinetic friction are two different types of friction. Static friction occurs when two surfaces are in contact with each other but not moving relative to each other. In this case, the tires of the car and the road are in contact but not moving relative to each other. Kinetic friction, on the other hand, occurs when two surfaces are in contact and sliding relative to each other. In the context of a car braking, both types of friction can be involved.

Now, let's look at the given information. The coefficient of static friction, denoted by the symbol "s", is a constant that represents the amount of friction between two surfaces in contact when there is no relative motion between them. In this case, the coefficient of static friction between the tires of the car and the road is given as s=0.56. This means that for every unit of force applied to the car, the road will exert a force that is 0.56 times the applied force in the opposite direction.

Next, the question asks for the maximum acceleration of the car when it is braked. This means that the net force on the car is equal to the force of static friction exerted by the road. This is because when the car is braked, the wheels stop turning and the car's motion is brought to a stop. This is where the coefficient of static friction comes into play. The maximum acceleration of the car can be calculated using the following formula:

a = s * g

Where "a" is the acceleration, "s" is the coefficient of static friction, and "g" is the acceleration due to gravity (9.8 m/s^2). Therefore, using the given coefficient of static friction (s=0.56), we can calculate the maximum acceleration of the car as:

a = 0.56 * 9.8 m/s^2 = 5.488 m/s^2

I hope this explanation helps to clarify the concept of static friction and its role in the braking of a car. Please let me know if you have any further questions. Thank you.