Coefficient of kinetic Friction given velocity and distance.

[pech0706]

Homework Statement

A car is moving with a velocity of 20m/s when the brakes are applied and the wheels lock (stop spinning), The car then slides to a stop in 40m. FInd the coefficient of kinitic friction between the tires and the road.

Homework Equations

F=ma
Ffriction=coefficient fo friction*N
N=mg

The Attempt at a Solution

I have drawn a picture and free body diagram, but that's as far as I've gotten. I'm stuck because I don't know how to calculate the normal force without the mass, and I don't now how to find the coefficient without N. I know the answer is 0.51, but I do not know how to get there.

 

[cupid.callin]

dont worry about mass.
take it as m
it will get canceled in the process.

 

[pech0706]

So, basically that means the total force acting on the car is the velocity and the frictional force. After ignoring the mass though, I'm still stuck. I don't know how to find the frictional force or the coefficent of friciton when ignoring mass.

 

[cupid.callin]

Dont ignore mass, take it as m.

Then do the general method and find the answer.
mass won't be any problem

 

[rwisz]

As a scientist, it is important to understand the principles and concepts behind the calculations, rather than just memorizing the answer. Let's break down the problem and see how we can approach it using the given information.

First, let's look at the forces acting on the car when the brakes are applied and the wheels lock. The only external force acting on the car is the force of friction between the tires and the road. This force is responsible for slowing down the car and ultimately bringing it to a stop. According to Newton's second law, this force is equal to the mass of the car times its acceleration (F=ma).

Next, we need to consider the normal force (N) acting on the car. This force is perpendicular to the surface of contact between the tires and the road and is equal to the weight of the car (N=mg). In this case, the weight of the car is acting downwards, while the normal force is acting upwards.

Now, let's look at the equation for friction: Ffriction=coefficient of friction*N. This equation tells us that the force of friction is directly proportional to the normal force and the coefficient of friction. The coefficient of friction is a dimensionless quantity that represents the roughness or smoothness of the surfaces in contact. It is a property of the two surfaces, not the individual objects.

So, how do we find the coefficient of friction in this problem? We can use the given information about the distance and velocity to determine the acceleration of the car. We know that the car starts at 20m/s and comes to a stop in 40m, so its initial velocity is 20m/s and its final velocity is 0m/s. Using the equation v^2=u^2+2as, we can calculate the acceleration (a) as -5m/s^2 (negative because the car is decelerating). Now, we can substitute this value into F=ma to find the force of friction.

F=ma
F=(-5m/s^2)(mass of the car)

We don't know the mass of the car, but we can cancel it out by dividing both sides by the mass:

F/m=(5m/s^2)
This equation tells us that the force of friction per unit mass (F/m) is equal to the acceleration of the car. But wait, we already know from the equation for friction that F/m=coefficient of friction*N.