Centripetal force of a rollercoaster

AI Thread Summary
The discussion focuses on calculating the force exerted by the track on a roller coaster wheel, given its mass, radius of the track, and speed. The mass of the roller coaster is 402 kg, the radius of the track is 70 m, and the speed is 45 m/s. Participants clarify that the scenario involves the coaster at the top of a loop, where both gravitational and centripetal forces play a role. The normal force is perpendicular to the surface and is influenced by the weight of the coaster and the required centripetal force. Understanding these forces is crucial for accurately determining the total force exerted by the track.
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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