Forces on an Inclined Plane Question

[catenn]

Hi I have a problem that reads: A car drives downhill on a road that is inclined 20 degrees to the horizontal. At a speed on 30 m/s the driver suddenly brakes until the car stops (coefficient of kinetic friction = .8, coefficient of static friction = .9).
A. When all of the wheels are locked, how far will the car skid over the road until it stops?
B. What is the steepest slope of a road on which a car can rest (with locked wheels) w/out slipping? Find the equation and maximum angle of the incline.

I began the problem and am not quite sure what to do. Once I drew the free body diagram I tried multiplying the 30 m/s by the .8 kinetic friction to get 24N of friction while the car still moves. It doesn't tell me how to find distance traveled though and there is no mass of the car given. I don't really know what to do with the coefficents and haven't used them yet in class. Also, for part B do we solve with an inverse cos or sin? Thanks.

 

[member 553083]

A. To find the distance the car will skid over the road until it stops, you need to use the equation for kinetic friction force (FK = μk*mg) and the equation for kinetic energy (K = ½mv^2). The mass of the car (m) can be calculated using the kinetic friction force equation, since you know the coefficient of kinetic friction (μk) and the acceleration due to gravity (g). Once you have the mass of the car, you can use the equation for kinetic energy to solve for the initial velocity (v) of the car before braking. With the initial velocity and the coefficient of kinetic friction, you can then calculate the total distance traveled by the car until it stops using the equation d = vt - (μk * g * t^2)/2.B. To find the maximum angle of the incline of a road on which a car can rest without slipping, you need to use the equation for static friction (FS = μs*mg). You know both the coefficient of static friction (μs) and the acceleration due to gravity (g), so you can calculate the maximum static friction force (FSmax) that the car can generate. With the maximum static friction force, you can then calculate the maximum angle of the incline (θ) using the equation θ = arctan (FSmax/ mg).