How Do You Calculate Speeds on a Banked Race Track Without Friction?

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Homework Help Overview

The discussion revolves around calculating the speeds of cars on a banked race track without friction, given specific dimensions such as the radii of the circular paths and the height of the outer wall. Participants are attempting to derive the necessary angle and speeds based on the provided measurements.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing the calculation of the angle of the banked track based on the height and width provided. There are attempts to use trigonometric relationships to find the angle and subsequently calculate the speed. Questions arise regarding the correctness of the calculations and the components of forces involved.

Discussion Status

The discussion is active, with participants sharing their calculations and questioning each other's methods. Some guidance has been offered regarding the use of the square root in the calculations, and there is an acknowledgment of potential errors in applying the net force components.

Contextual Notes

Participants note the absence of angles in the initial problem statement, which has led to some confusion and assumptions about the track's geometry. The reliance on frictionless conditions is also a key aspect of the problem being explored.

Miss1nik2
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On a banked race track, the smallest circular path on which cars can move has a radius of 111 m, while the largest has a radius of 157 m, as the drawing illustrates. The height of the outer wall is 15.7 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.


I am having trouble finding an answer because I wasnt given any angles. Please help me in any way that you can. Thank you VERY much!
 
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Miss1nik2 said:
On a banked race track, the smallest circular path on which cars can move has a radius of 111 m, while the largest has a radius of 157 m, as the drawing illustrates. The height of the outer wall is 15.7 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.


I am having trouble finding an answer because I wasnt given any angles. Please help me in any way that you can. Thank you VERY much!
You didn't attach a picture, but I believe that the track is sloped at an angle that has a 15.7m rise over the track width of (157m -111m) = 46m. From that, you should be able to detremine the angle.
 
Using that information I found the angle to be 18.85 degrees. And I found the answer to part (a) 371.38. But that answer is not correct.

Do you know what I did wrong? Any additional help?? Thank you...
 
And I found the answer to part (a) 371.38. But that answer is not correct.

Did you remember about the square root?
 
Miss1nik2 said:
Using that information I found the angle to be 18.85 degrees. And I found the answer to part (a) 371.38. But that answer is not correct.

Do you know what I did wrong? Any additional help?? Thank you...
your angle looks good. I didn't see your work or check out the math on my own, but you may have used the wrong component of net force in the horizontal direction. What did you use, and why?
 
I used the equation v= sq.rt. r*g*tan (theta)

So, my work for part a is...

sq. rt. (111)(9.8)tan(18.85) = 371.38.

The computer tells me that is the wrong answer...
 
hage567 said:
Did you remember about the square root?
oh, yeah, should've done the math...take the sq root...
 
It worked! THANK YOU! I guess I did forget to take the sq rt. Thank you both.
 

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