Consider a roller-coaster car on a track that has a loop of known radius R. If there is no friction between the rollercoaster car and the track, then determine (a) the minimum speed at the top of the loop for the rollercoaster car to still be in contact with the track and (b) the minimum height h the rollercoaster car must start from in order to go all the way around the loop without losing contact with the track (assuming the rollercoaster starts from rest). The only knowns here are R and g, so your symbolic answers need to be in terms of these. Part (a) can be treated using newton's second law and uniform circular motion (even though it's not really uniform). Start with a free-body diagram of a coaster car at the top of the loop.What does it mean for the rollercoaster car to still be "in contact" with the track?Part (b) can be treated using conservation of mechanical energy. You'll need your result from part (a).How high above the ground are you when you're at the top of the loop? The image depicts a diagram of a roller coaster track. The track starts with an initial vertical height \( h \), descends into a dip, and then loops into a vertical circle. The vertical circle has a radius \( R \). A point on the circle is marked to indicate the center of the loop.The diagram is used to demonstrate concepts of energy conservation and centripetal force in a physics context. Starting from height \( h \), potential energy is converted into kinetic energy as the object moves downwards. As the object enters the loop with radius \( R \), it demonstrates the need for a certain speed to maintain contact with the track due to centripetal force acting towards the center of the circle. The diagram is essential for understanding motions on curved tracks and the dynamics involved.

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Answered: Consider a roller-coaster car on a…

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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Consider a roller-coaster car on a track that has a loop of known radius R. If there is no friction between the rollercoaster car and the track, then determine (a) the minimum speed at the top of the loop for the rollercoaster car to still be in contact with the track and (b) the minimum height h the rollercoaster car must start from in order to go all the way around the loop without losing contact with the track (assuming the rollercoaster starts from rest). The only knowns here are R and g, so your symbolic answers need to be in terms of these.

Part (a) can be treated using newton's second law and uniform circular motion (even though it's not really uniform).
Start with a free-body diagram of a coaster car at the top of the loop.
What does it mean for the rollercoaster car to still be "in contact" with the track?
Part (b) can be treated using conservation of mechanical energy. You'll need your result from part (a).
How high above the ground are you when you're at the top of the loop?

The image depicts a diagram of a roller coaster track. The track starts with an initial vertical height \( h \), descends into a dip, and then loops into a vertical circle. The vertical circle has a radius \( R \). A point on the circle is marked to indicate the center of the loop.

The diagram is used to demonstrate concepts of energy conservation and centripetal force in a physics context. Starting from height \( h \), potential energy is converted into kinetic energy as the object moves downwards. As the object enters the loop with radius \( R \), it demonstrates the need for a certain speed to maintain contact with the track due to centripetal force acting towards the center of the circle. The diagram is essential for understanding motions on curved tracks and the dynamics involved.

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