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A 2000 kg rollercoaster starts from rest at a height of 100 meters from the bottom...

  1. A 2000 kg rollercoaster starts from rest at a height of 100 meters from the bottom of a loop the loop with a radius R. What is the largest value of R such that the rollercoaster will make it around the loop?
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Answer #1

If the rollercoaster remains in contact at the top of the loop where the normal force is minimum, it will remain in contact everywhere and make it around the loop. We use Newton’s law of motion at top of the loop for vertical circular motion to find the minimum speed needed and then use conservation of energy principle to find the value of radius as shown below

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