Roller coaster rider weight problem

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Homework Help Overview

The problem involves calculating the apparent weight of a roller coaster rider at the bottom of a vertical loop with a specified radius. The context is centered around concepts of centripetal force and gravitational force, particularly in the realm of dynamics and circular motion.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between centripetal acceleration and gravitational force, questioning the comparison of their units. There is also a reference to personal experiences in vehicles to illustrate the feeling of weight changes during motion.

Discussion Status

The discussion is exploring the differences between centripetal force and gravitational force, with some participants providing personal insights and experiences to support their reasoning. There is an acknowledgment of the need to determine how much greater the apparent weight is at the bottom of the loop, indicating a productive line of inquiry.

Contextual Notes

Participants note the importance of the roller coaster's speed and the height from which it descends, suggesting that these factors are crucial for further calculations but are currently not provided in the problem statement.

Cisneros778
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Homework Statement


Suppose the vertical loop has a radius of 6.81 m. What is the apparent weight (Wap) of a rider on the roller coaster at the bottom of the loop? (Assume that friction between roller coaster and rails can be neglected. Give your answer in terms of m and g.)

R = 6.81 m

Homework Equations


F=m(a_c)

The Attempt at a Solution


Since the roller coaster is at the bottom the centripetal acceleration should be smaller than the weight of the rider on the roller coaster... I think...
 
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Cisneros778 said:

Homework Statement


Suppose the vertical loop has a radius of 6.81 m. What is the apparent weight (Wap) of a rider on the roller coaster at the bottom of the loop? (Assume that friction between roller coaster and rails can be neglected. Give your answer in terms of m and g.)

R = 6.81 m

Homework Equations


F=m(a_c)

The Attempt at a Solution


Since the roller coaster is at the bottom the centripetal acceleration should be smaller than the weight of the rider on the roller coaster... I think...

For a start "centripetal acceleration" is an acceleration - units ms-2 and "weight of the rider" is a force - units N so I am not sure what you mean that one will be less than the other. Like saying I a taller than you weigh!

Secondly - ever been in a car that drives through a dip? Did you feel lighter or heavier at the time?
 
Sorry I meant centripetal force vs. the force of gravity. I don't really pay much attention while I'm in a car driving through loops. I reckon you are heavier.
 
Cisneros778 said:
Sorry I meant centripetal force vs. the force of gravity. I don't really pay much attention while I'm in a car driving through loops. I reckon you are heavier.

That is correct, so from your own experience you already know that the answer to this question will be that your apparent weight is greater at the bottom.
The next difficulty is - how much bigger?

As far as the centripetal force is concerned, the size of that depends on how fast you are going. You do know that Fc = mv2/R

Now if you knew from what height the cart had come from you could use the transformation of PE to KE to work that out.

PEtop → KEbottom

so mgh → 0.5mv2

so mv2 = 2mgh → mv2/R = 2mgh/R
 

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