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Chapter 4: Q64. (page 105)

On an icy day, you worry about parking your car in your driveway, which has an incline of 12掳. Your neighbor鈥檚 driveway has an incline of 9.0掳, and the driveway across the street is at 6.0掳. The coefficient of static friction between tire rubber and ice is 0.15. Which driveway(s) will be safe to park in?

Short Answer

Expert verified

Only the driveway across the street is safe for parking.

Step by step solution

01

Step 1. Given data 

The coefficient of static friction is 渭s=0.15.

Let the mass of the car be mand the angle of incline be 胃.

02

Step 2. Calculation of safe parking 

The car can be parked safely where the static friction force is more than the sine component of the weight.

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

The frictional force on the car is:

fs=渭sN=渭smgcos胃

The condition for safe parking is:

mgsin胃鈮�fsmgsin胃鈮�渭smgcos胃tan胃鈮�渭s胃鈮�tan-1渭s

Now, substituting the value, you will get:

胃鈮�tan-1渭s胃鈮�tan-10.15胃鈮�8.53掳

Hence, only the driveway across the street is safe for parking because it has an inclination of (6掳), which is less than 8.53掳.

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