Centripetal force of a rollercoaster

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SUMMARY

The discussion focuses on calculating the force exerted by the track on a roller coaster wheel at the top of a loop. Given a mass of 402 kg, a radius of 70 m, and a speed of 45 m/s, the participants clarify that both gravitational force and centripetal force contribute to the normal force at this point. The correct approach involves calculating the gravitational force and the centripetal force, then summing these to determine the total normal force acting on the wheel.

PREREQUISITES
  • Centripetal force concepts
  • Free Body Diagrams (FBD)
  • Newton's laws of motion
  • Basic physics of roller coasters
NEXT STEPS
  • Calculate gravitational force using the formula F = mg
  • Determine centripetal acceleration with a = v²/r
  • Learn how to sum forces in Free Body Diagrams
  • Explore the dynamics of roller coasters at different points in a loop
USEFUL FOR

Physics students, engineers, and anyone interested in the mechanics of roller coasters and centripetal motion.

dkgojackets
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"The wheels of a certain roller coaster are both above and below the rails so that the car will not leave the rails. The mass supported by this particular wheel is 402 kg and the radius of this section of track is 70 m. What is the magnitude of the force that the track exerts on the wheel when the speed of the car is 45 m/s?"

I'm not sure where to go. I've tried finding the centripetal acceleration and multiplying it by 402, but it was wrong. I have a FBD but don't know what to do from here.
 
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dkgojackets said:
"The wheels of a certain roller coaster are both above and below the rails so that the car will not leave the rails. The mass supported by this particular wheel is 402 kg and the radius of this section of track is 70 m. What is the magnitude of the force that the track exerts on the wheel when the speed of the car is 45 m/s?"

I'm not sure where to go. I've tried finding the centripetal acceleration and multiplying it by 402, but it was wrong. I have a FBD but don't know what to do from here.
Is the coaster at the top of the curve or at the bottom? The weight of the coaster as well as the normal force will contribute to the centripetal force.
 
It is at the top of the loop.

Normal force I know is perpendicular to the surface, so would it just be the sum of weight and the centripetal force down?
 

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