What is the speed of the roller coaster at the bottom of the dip?

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Homework Help Overview

The problem involves a roller coaster navigating a dip that forms a vertical circle, with a focus on the forces acting on a passenger at the bottom of the dip. The subject area pertains to dynamics and circular motion.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of forces acting on the passenger, particularly the normal force and gravitational force. There is a focus on correctly interpreting the relationship between mass and weight in the context of the forces involved.

Discussion Status

Participants are actively clarifying the correct expressions for forces and ensuring that the original poster understands the distinction between mass and weight. There is a productive exchange regarding the setup of the equations, with some guidance being offered on how to correctly apply the forces.

Contextual Notes

There is an emphasis on the correct interpretation of the forces involved, particularly in relation to the passenger's weight and the normal force experienced at the bottom of the dip. The original poster initially misapplied the concept of mass versus force, which has been acknowledged and corrected in the discussion.

Amber430
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A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to three times her weight as she goes through the dip. If r = 22.0 m, how fast is the roller coaster traveling at the bottom of the dip?

At the bottom of the dip, Fn -mg= m(v^2/r). I plugged in 3m for Fn since it's 3 times her weight, and I'm not sure if I'm doing this right.
 
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Amber430 said:
At the bottom of the dip, Fn -mg= m(v^2/r).
Good.
I plugged in 3m for Fn since it's 3 times her weight, and I'm not sure if I'm doing this right.
Careful. 3m is a mass, not a force. What's her weight? What's 3 times her weight?
 
It looks like everything you have done is correct. When you say that you plugged in 3m for Fn you mean (3m)*g, right? If so, it looks correct.
 
No, I was not using 3mg, just 3m. That's where I messed it up. It makes sense now, thank you so much!
 

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