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The minimum coefficient of static friction needed if the car is to navigate the curve without slipping.
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Answer to Problem 32P
The minimum coefficient of static friction needed if the car is to navigate the curve without slipping is
Explanation of Solution
Figure 1 shows the free body diagram of the car.
Write an expression to calculate the net horizontal force.
Here, the normal force is
Write an expression for the net vertical force.
Here, the acceleration due to gravity is
Neglect the frictional force and rewrite equation (I).
Neglect the frictional force and rewrite equation (II).
Rearrange equation (IV) to find
Substitute equation (V) in equation (III).
Rewrite equation (VI) to find
Now consider the presence of frictional force.
Rearrange equation (I) to find
Rearrange equation (II) to find
Compare equation (VIII) and (IX).
Rearrange equation (X) to find
Conclusion:
Substitute
Substitute
Thus, the minimum coefficient of static friction needed if the car is to navigate the curve without slipping is
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