Question

A car roles down a driveway (10 degress above horizontal; length 10m) from rest without slipping. Assuming a coefficient of friction of f=0.1. What is the speed of the car (parallel to the incline) at the bottom of the incline? What is the maximum angle such that the car does not role down the incline?

Answer 1

(a)

let's find the acceleration of the car along the incline = g * sin(theta) - mu * g * cos(theta)

a = 9.81 * sin(10) - 0.1 * 9.81 * cos(10) = 0.7374 m/s^2

initial velocity on top = 0

let final velocity at the bottom of incline be v

using v^2 - u^2 = 2 * a * s

v^2 = 2 * 0.7374 * 10

=> v = 3.84 m/sec

The speed of the car at the bottom of the incline is 3.84 m/sec

(b)

let the angle be theta

To not roll down, the weight component along incline should balance the frictional force

=> m * g * sin(theta) = mu * m * g * cos(theta)

=> tan(theta) = mu => theta = arctan(mu)

=> theta = 5.71 degrees

The maximum angle such that the car does not roll down is 5.71 degrees