Solve a radial acceleration problem?

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Discussion Overview

The discussion revolves around solving a radial acceleration problem related to a car traversing a bump. Participants explore the necessary knowns to determine the radius of the bump, considering various forces and conditions involved in the scenario.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the minimum knowns required to solve for the radius of a bump when only the speed of the car is provided.
  • Another participant suggests a specific scenario where the speed is given, prompting a calculation for the smallest radius bump that allows the car to maintain contact with the road.
  • Concerns are raised about how to approach the problem with limited information, particularly regarding the relationship between radial acceleration and speed.
  • There is a debate about whether the problem is asking for the smallest or largest radius bump, with one participant suggesting that a radius of zero could be a solution for the smallest bump.
  • Participants discuss the forces acting on the car, including the normal force and weight, and how they contribute to maintaining contact with the bump.
  • Clarifications are made regarding the nature of the forces at play, particularly at the limit where the normal force approaches zero.

Areas of Agreement / Disagreement

Participants express differing views on whether the problem pertains to the smallest or largest radius bump, indicating a lack of consensus. Additionally, there is uncertainty about how to approach the problem with the given information.

Contextual Notes

Participants highlight the need for clarity on the definitions of radius in this context, as well as the assumptions regarding forces acting on the car. The discussion does not resolve these ambiguities.

Who May Find This Useful

This discussion may be of interest to those studying mechanics, particularly in relation to circular motion and forces acting on objects in motion.

Alem2000
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I wanted to konw what is the least amount of knowns you need to solve a radial acceleration problem? My friend told me he was given a problem where a care was traveling over a bump and the only known he had was the speed of the care, no radious, no nothing. And the question was to solve for radius...that seems hard is it possilbe to get a numerical value?
 
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One version of such a question goes like this: Given a speed v, what is the smallest radius bump (that is, the sharpest bump) that the car could traverse without losing contact with the road?

Give it a try.
 
okay, given a speed[tex]v[/tex] what is the [tex]r_m[/tex] where the sub m is min
hmm well [tex]F=m(v^2/r_m)[/tex]... i don't know! I don't understandt how can you solve with one given? you have the radial acceleration which would be pointing inward, and you have your speed[tex]v[/tex] pointing tangent to the path. Could you relate the sum of forces in the y direction and the x direction to cancel out terms? :frown:
 
Doc Al,

Maybe I'm misunderstanding, but wouldn't it be the largest radius bump? If it is the smallest radius bump, I could say the radius is zero and there would be no bump? Or am I lost?

Moooooo
 
I was going to say [tex]v^2/r=4\pi r/t^2[/tex] but i don't have time either do i?
 
Alem2000 said:
okay, given a speed[tex]v[/tex] what is the [tex]r_m[/tex] where the sub m is min
hmm well [tex]F=m(v^2/r_m)[/tex]... i don't know!
So far, so good. Now what force is providing the "centripetal" force? (What forces act on the car?)
 
Moose352 said:
Maybe I'm misunderstanding, but wouldn't it be the largest radius bump? If it is the smallest radius bump, I could say the radius is zero and there would be no bump? Or am I lost?
Well, I know what you mean... if the radius were 1 cm, it would just be like rolling over a pebble. :smile:

But that's not the way to think of this. What's the radius of curvature of a flat road? Not zero! Think of a spherical balloon being inflated. As it inflates, r increases but the surface becomes flatter. A perfectly flat road would have infinite radius.
 
what force? the normal force? Yeah i guess, with friction would keep it in a curcular path... :shy:
 
Friction, eh? :rolleyes:

The forces acting vertically are the weight (down) and the normal force (up). At the limit before the car loses contact, the normal force goes to zero. So the only force acting on the car, and keeping it in contact with the bump, is its weight.
 

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