(a)
The forceexerted by the track on the fully loaded roller-coaster at point
(a)
Answer to Problem 16P
The forceexerted by the track on the fully loaded roller-coaster at point
Explanation of Solution
Consider the fully loaded roller-coaster car is moving on a curved path which has a radius of curvature. If the roller-coaster car rotates on a circular path, then it experiences a force acts towards the center of the circle which is known as
The magnitude of centripetal force
- 1. The speed of the roller-coaster car.
- 2. The mass of the roller-coaster car.
- 3. The radius of curvature of the curve path.
The forces act on the fully loaded roller-coaster car when it is at point
Write the expression for the fully loaded roller-coaster car corresponding to Newton’s second law in
Here,
Write the expression for centripetal acceleration as.
Here,
Substitute
Simplify the above expression for
Conclusion:
Substitute
Thus, the force exerted by the track on the fully loaded roller-coaster at point
(b)
The maximum speed the vehicle can have at point
(b)
Answer to Problem 16P
The maximum speed the vehicle can have at point
Explanation of Solution
The direction of the centrifugal force and the normal force exerted by the track on the fully loaded roller-coaster is in same direction. As the speed of the car increases, the centripetal force increase which results decrease in normal reaction force.
The car keeps on track because of normal force reaction exerted by the track on the car.
At the verge to keep the car on the track, the normal force exerted by the track on the car is equal to zero. If the normal reaction force is equal to zero, then weight of the car will be equal to the centripetal force.
Write the expression for the condition of a car to keep on the track as.
Here,
Write the expression for centrifugal force acts on the car at point
Here,
Substitute
Re-arrange the terms
Simplify the above expression for
Conclusion:
Substitute
Thus, the maximum speed the vehicle can have at point
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Chapter 6 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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