An unpowered roller-coaster car starts at rest at the top of a hill of height H, rolls down the hill, then then goes around a vertical loop of radius R. Determine the minimum value for H required if the car is to stay on the track at the top of the loop. (Hints: At the top of the loop, the car is upside-down. If it is in contact with the track, though, the contact interaction will exert a normal force on the car perpendicular to the track and away from the track since the normal force is a compression force. You may find it useful to use conservation of energy here!)

An unpowered roller-coaster car starts at rest at the top of a hill of height H, rolls down the hill, then then goes around a vertical loop of radius R. Determine the minimum value for H required if the car is to stay on the track at the top of the loop. (Hints: At the top of the loop, the car is upside-down. If it is in contact with the track, though, the contact interaction will exert a normal force on the car perpendicular to the track and away from the track since the normal force is a compression force. You may find it useful to use conservation of energy here!)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

10.3 An unpowered roller-coaster car starts at rest at the top of a hill of height H, rolls down the hill, then
then goes around a vertical loop of radius R. Determine the minimum value for H required if the car
is to stay on the track at the top of the loop.
(Hints: At the top of the loop, the car is upside-down. If it is in contact with the track, though, the
contact interaction will exert a normal force on the car perpendicular to the track and away from the
track since the normal force is a compression force. You may find it useful to use conservation of energy
here!)
6.

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