Banked Curve Without Friction

  • Thread starter eestep
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  • #1
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Homework Statement


A car is traveling around a circular, banked track without friction. It is initially traveling around bottom of ramp where inner radius of track is 397 meters. Car then increases its velocity by a factor of 1.9. If inclination angle is 13 degrees, what is height (vertical distance above ground) car is traveling at this new velocity? Answer is 239.22 meters.


Homework Equations


v=[tex]\sqrt{}Rgtan\theta[/tex]


The Attempt at a Solution


v=[tex]\sqrt{}(397)(9.81)tan(13)[/tex]=29.99
 
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Answers and Replies

  • #2
648
2
You have correctly calculated the velocity of the car initially at the bottom of the ramp.
Now increase that velocity by a factor of 1.9 and calculate the new value of r, using your formula. This will tell you, by trigonometry, how far up the slope the car needs to be.
[are you certain the increase is "a factor of 1.9", it seems a lot; almost double]
 
  • #3
36
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After calculating R, do I determine height by multiplying it times tan(13)? I am certain but am getting 330.96.
 
  • #4
648
2
Yes. The vertical height up the slope is x tan 13
where x is the increase in the radius.
 
  • #5
36
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Thank you!
 

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