Circular Motion. Roller-coaster mass of car and max speed

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Homework Help Overview

The discussion revolves around a roller-coaster problem involving circular motion, specifically focusing on the mass of the car at point A and the maximum speed at point B while considering gravitational forces. Participants are exploring the dynamics of forces acting on the roller-coaster car as it navigates through different points on the track.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of relevant equations for circular motion, particularly in relation to forces at points A and B. There is an emphasis on understanding how gravitational force influences the car's motion and the conditions necessary for it to remain on the track.

Discussion Status

Some participants are attempting to clarify their understanding of the forces acting on the car, particularly at point B. Guidance has been offered regarding the use of free-body diagrams to visualize the forces involved, and there is an ongoing exploration of how to manipulate the equations to find the maximum speed without reaching a consensus on the solution.

Contextual Notes

Participants note confusion regarding the application of equations and the roles of different forces at point B, particularly questioning the necessity of the normal force when only gravitational force is acting on the car. There is also mention of previous classroom discussions that may influence their current understanding.

AStupidHippo
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Homework Statement


A roller-coaster car speeds down a hill pas point A and then rolls up a hill past point B.
A. Car speed = 20 m/s at point A. If the track exerts a normal force on the car of 2.06x10^4N at this point, what is the mass of the car? (account for gravitational force)
B. What is the maximum speed the car can have at point B for the gravitational force to hold it on the track?
Diagram(I made it myself): http://gyazo.com/0415a6ba75f87f0229e08aab0f68fbe1

Homework Equations


Circular motion
Fc= (mv^2)/r
Fn-mg= (mv^2)/r

The Attempt at a Solution


Completely lost.
 
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AStupidHippo said:

Homework Statement


A roller-coaster car speeds down a hill pas point A and then rolls up a hill past point B.
A. Car speed = 20 m/s at point A. If the track exerts a normal force on the car of 2.06x10^4N at this point, what is the mass of the car? (account for gravitational force)
B. What is the maximum speed the car can have at point B for the gravitational force to hold it on the track?
Diagram(I made it myself): http://gyazo.com/0415a6ba75f87f0229e08aab0f68fbe1

Homework Equations


Circular motion
Fc= (mv^2)/r
Fn-mg= (mv^2)/r

The Attempt at a Solution


Completely lost.
I don't know why you are lost because your relevant equations are quite relevant for part A, assuming point A is at the bottom of dip. Solve for m.
 
I should have clarified.We did most of A in class, B. is where I'm struggling at most.
 
AStupidHippo said:
I should have clarified.We did most of A in class, B. is where I'm struggling at most.
Ok, got it. For part B, the question asks for the max speed at point B if the only force in the vertical direction acting on the coaster at that point on the top of the curve is the gravity (weight) force that is keeping it on the track in centripetal motion, without flying off it. You should be able to manipulate your relevant equations to solve for that speed.
 
Can you draw a free-body diagram for the cart at point B to help you out? What forces are acting on the cart?
 
I don't think I can solve this problem using fn-mg=(mv^2)/r. The Ms would just cancel out?
 
"Can you draw a free-body diagram for the cart at point B to help you out? What forces are acting on the cart?"
It would be G only. Correct?
Jason Healy said:
Can you draw a free-body diagram for the cart at point B to help you out? What forces are acting on the cart?
It would be G only, correct?
 
AStupidHippo said:
I don't think I can solve this problem using fn-mg=(mv^2)/r. The Ms would just cancel out?
if only the gravity force is acting , what is fn? Let the m's cancel if they do. Now watch your signage. Draw a free body diagram. Net centripetal force is always in direction of the centripetal acceleration,
 

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