Why is the normal force on a roller coaster's peak greater than mg?

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The normal force on a roller coaster at the top of a loop is greater than the gravitational force (mg) to ensure riders remain securely in their seats. At the peak of a loop, the track exerts a downward force that must counteract both gravity and provide the necessary centripetal force to keep the coaster on the track. Conversely, at the top of a hill, the normal force is less than mg, and if the coaster's speed is insufficient, it could lead to a loss of contact with the track. The discussion clarifies that the context of the coaster's position—whether at a loop or a hill—significantly affects the normal force experienced. Understanding these dynamics is crucial for roller coaster design and rider safety.
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Why is the normal force on the top of roller coster greater then mg?
 
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You mean at the top of a loop? Because if it's at the top of a hill it isn't.
 
Are you talking about the coaster on the inside of a loop at the top where the track would be pushing it down or the coaster being at the top of a hill where the track would be below the coaster?
 
If you were in a loop, and the force of gravity was greater than the normal force, you'd fall out of the ride.

If however you were going over the hill where the track was below you, the normal force would be less and if you were going fast enough, gravity wouldn't be enough to keep you on the track and you would fly off as a projectile.
 
Yes that's exactly what i was finding for.thanks bro:)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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