Kinetic Friction: Stopping a 2500kg Car on Icy Road

[cowasocke]

you are driving a 2500.0 kg car at constant speed of 14.0 m/s on a straight, level, icy road. you slam on brakes and stop after 25.0 m. what is coefficient of kinetic friction between your tires and the icy road?

 

[daniel_i_l]

Show some work first!
Hint: F = ma.

 

[quicknote]

The coefficient of kinetic friction between the tires of the car and the icy road can be calculated using the equation F = μkN, where F is the force of friction, μk is the coefficient of kinetic friction, and N is the normal force. In this scenario, the normal force would be equal to the weight of the car, which can be calculated using the equation Fg = mg, where m is the mass of the car and g is the acceleration due to gravity.

Using the given information, we can calculate the force of friction by first finding the initial kinetic energy of the car, which is equal to ½mv^2, where m is the mass of the car and v is the initial velocity. In this case, the initial kinetic energy would be (1/2)(2500.0 kg)(14.0 m/s)^2 = 245,000 J. Since the car comes to a stop, all of this kinetic energy is converted into frictional energy, so the force of friction would be equal to 245,000 J.

Next, we can calculate the normal force by multiplying the mass of the car by the acceleration due to gravity, which is approximately 9.8 m/s^2. Therefore, the normal force would be (2500.0 kg)(9.8 m/s^2) = 24,500 N.

Now, we can plug in these values into the equation F = μkN and solve for μk. This would give us μk = F/N = 245,000 J/24,500 N = 10. This coefficient of kinetic friction seems unusually high, which could be due to the icy road surface. It is important to note that the coefficient of kinetic friction can vary depending on the surface and conditions, so this value may not be representative of all icy roads.

In conclusion, the coefficient of kinetic friction between the tires of the car and the icy road in this scenario is approximately 10. Further experimentation and data collection would be necessary to accurately determine the coefficient of kinetic friction for icy roads.