Problem 14PE

Calculate the maximum acceleration of a car that is heading up a 4º slope (one that makes an angle of 4º with the horizontal) under the following road conditions. Assume that only half the weight of the car is supported by the two drive wheels and that the coefficient of static friction is involved—that is, the tires are not allowed to slip during the acceleration. (Ignore rolling.) (a) On dry concrete. (b) On wet concrete. (c) On ice, assuming that μs = 0.100 , the same as for shoes on ice.

Solution 14PE

We are required to calculate the maximum acceleration of the car under different road conditions.

Step 1of 2

Let us resolve the forces acting on the car and to do this let draw a figure as shown below.

We are required to consider half the weight of the car here. If the car has to keep moving up the inclined plane, the force upward the plane must be greater than the downward force

The maximum force in this case is given by,

…..(1)

Maximum acceleration