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Chapter 4: Q39. (page 103)

The coefficient of static friction between hard rubber and a normal street pavement is about 0.90. On how steep a hill (maximum angle) can you leave a car parked?

Short Answer

Expert verified

You can park the car at the maximum angle of 41.99掳.

Step by step solution

01

Step 1. Given data and assumption

The car can be parked when the static friction force is greater than or equal to the sin component of the car's weight.

Given data:

The coefficient of the static friction between the regular street pavement and rubber is 渭s=0.90.

Assumption:

Let 胃be the maximum angle of the slope.

Let m be the mass of the car.

02

Step 2. Components of forces on the car 

03

Step 3. Calculation of the coefficient of static friction

The normal force acting on the car is N=mgcos胃.

The static friction force is

fs=渭sN=渭smgcos胃

Here, the car does not slide after parking. So,

mgsin胃=fsmgsin胃=渭smgcos胃tan胃=渭s胃=tan-1渭s

Now, substituting the value of 渭sin the above equation,

胃=tan-10.90=41.99掳

Hence, you can park the car at a maximum angle of41.99掳.

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