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## 4.A student with a mass of m rides a roller coaster with a loop with a radius of curvature of r. What is the minimum speed the rollercoaster

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4.A student with a mass of m rides a roller coaster with a loop with a radius of curvature of r. What is the minimum speed the rollercoaster can maintain and still make it all the way around the loop

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Physics
3 years
2021-08-18T13:47:13+00:00
2021-08-18T13:47:13+00:00 1 Answers
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## Answers ( )

Answer:v = √gr

Explanation:In order for the roller coaster to make it all the way around the loop, the centripetal force at the top of the rider must be equal to the weight the student. So, that the student does not fall during the motion. Therefore,

Centripetal Force = Weightmv²/r = mgv²/r = gv² = grTaking square root on both sides, we get:

v = √grwhere,

v = speed of roller coaster

r = radius of curvature

g = acceleration due to gravity

Hence, the minimum speed the roller coaster can maintain and still make it all the way around the loop, is found to be:

v = √gr