Concept explainers
Banked curves are designed so that the radial component of the normal force on the car rounding the curve provides the
(a)
The magnitude of range of velocities.
Answer to Problem 59PQ
The range of velocities are
Explanation of Solution
Case 1:
When the car slips down towards the inclined plane, then the frictional force is directed up from the inclined plane.
Write the expression for the y-component force on the car.
Here,
Write the expression to calculate the static frictional force on the car.
Here,
Substitute the above equation in (I) to calculate
Write the expression for the x-component of force on the car.
Here,
Substitute the expression for
Substitute
Case 2:
When the car is slip up the incline plane the frictional force is directed towards down the incline plane.
Write the expression for the y-component force on the car.
Substitute the equation for f in (II) to calculate
Write the expression for the x-component of force on the car.
Here,
Substitute the expression for
Substitute
Conclusion:
Therefore, the range of velocities are
(b)
The minimum value for
Answer to Problem 59PQ
The minimum value for
Explanation of Solution
Write the expression for minimum speed for the car.
Equate the above equation to zero to calculate the expression for
Substitute
Conclusion:
Therefore, the minimum value for
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