Solving Kinetic Friction: Find Coefficient of Friction from Car Stop

[mels]

Homework Statement

A car is moving with a speed of 20m/s when the brakes are applied. The wheels lock (stop spinning). After traveling 40m, the car stops. Determine the coefficient of kinetic friction between the tires and the road.

Homework Equations

Fk=uk x Fn

The Attempt at a Solution

I don't know how to encorporate the given into the equation !

 

[Platformance]

There's another equation you need, one that puts all the given data together.

 

[raghav singh]

You can apply simple formula...

calculate the acceleration 'a'... by
(square of final velocity)-(square of initial velocity)=2x a x distance

a=20x20/(2x40)
a=5

balance the force
uk x mass x g = mass x a
uk=a/g
uk=5/10=0.5

 

[mels]

okay thank you ! i really appreciate it :)

 

[Nickie]

To solve for the coefficient of kinetic friction, we can use the equation Fk=uk x Fn, where Fk is the kinetic friction force, uk is the coefficient of kinetic friction, and Fn is the normal force between the tires and the road.

First, we need to determine the normal force. Since the car is on a flat surface, the normal force will be equal to the weight of the car, which we can calculate using the mass of the car and the acceleration due to gravity (9.8 m/s^2).

Next, we need to determine the kinetic friction force. This is the force that opposes the motion of the car and causes it to stop. We can calculate this by using the equation Fk=ma, where m is the mass of the car and a is the acceleration. In this case, the acceleration is equal to the initial velocity (20m/s) squared divided by the distance traveled (40m). This will give us the kinetic friction force.

Finally, we can plug in the values we have calculated into the equation Fk=uk x Fn and solve for uk. This will give us the coefficient of kinetic friction between the tires and the road.

It is important to note that there may be other factors at play that can affect the coefficient of friction, such as the condition of the road surface and the type of tires on the car. Therefore, the calculated coefficient of kinetic friction may not be entirely accurate, but it can still give us a good estimate.