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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
The figure 1 shows the free body diagram of the car.
Write an expression to calculate the net horizontal force.
Here,
Write an expression for the net vertical force.
Here,
Neglect the frictional force and re-write equation (I)
Neglect the frictional force and re-write equation (II)
Re-arrange equation (IV) to find
Substitute equation (V) in equation (III),
Rewrite equation (VI) to find
Now consider the presence of frictional force.
Re-arrange equation (I) to find
Re-arrange equation (II) to find
Compare the expression (VIII) and (IX) and rearrange the equation to find
Conclusion:
Substitute
Substitute
Therefore, the minimum coefficient of static friction needed if the car is to navigate the curve without slipping is
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