Concept explainers
In Prob. 13.42. determine the range of values of h for which the roller coaster will not leave the track at D or E, knowing that the radius of curvature at E is
The range of values of h for which the roller coaster will not leave the track.
Answer to Problem 13.43P
The value of range of h is 50ft
Explanation of Solution
Given information:
Radius of curvature at point E is=75ft.
Consider free body diagram of the roller coaster at point D.
Resolve the forces acting on the rider by Newton’s second law.
Apply the principle of work and energy to the roller coaster at point A and point D.
Find the resultant acceleration acting on the coaster at the point B is
The coaster is at rest at position A,
Kinetic energy of the rider at point D is,
Work done by the rider in reaching position D from position A,
Substitute above values we get,
Resultant acceleration acting on the rider at point D travelling in a circular track with radius of curvature r.
The normal force acting on the coaster at point D should be greater than zero.
For the roller coaster to not leave the track,
Consider free body diagram roller coaster at point E as shown below:
Resultant acceleration acting on the roller coaster at the point E downwards is
Resolve the forces acting on the coaster by Newton’s second law at point E.
Apply the principle of work and energy to the roller coaster at point A and point E.
Find the resultant acceleration acting on the coaster at the point E is
The coaster is at rest at position A.
Kinetic energy of the rider at point E is,
Work done by the rider in reaching position E from position A.
Substituting the above values we get,
Resultant acceleration acting on the rider at point E travelling in a circular track with radius of curvature
The normal force acting on the coaster at point E should be greater than zero.
For the roller coaster to not leave the track,
Substituting the above values we get,
The range of values for h is
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Chapter 13 Solutions
Vector Mechanics For Engineers
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