Cushion seat angle : Radius of curvature

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Discussion Overview

The discussion revolves around a physics problem related to the angle of a cushion seat in a moving car, specifically focusing on the radius of curvature and its relevance to the forces acting on the seat. Participants are exploring the setup of the problem, including free body diagrams (FBD) and the effects of acceleration due to the car's motion.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks a hint on how to set up the solution, indicating they understand the scenario without motion.
  • Another participant questions the relevance of the radius of curvature and the car's speed to the problem.
  • A participant describes their approach using forces on the box, breaking them down into components and deriving an angle of 10.87°.
  • There is a suggestion to attach a free body diagram to aid in understanding the forces involved.
  • Some participants discuss the additional acceleration due to the car's motion, suggesting that it should be included in the analysis.
  • Questions arise about the nature of the additional acceleration, with references to tangential and normal components.
  • One participant expresses uncertainty about their calculations, arriving at an angle of 3.8° and seeking feedback on their FBD.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the relevance of the radius of curvature and the speed of the car, as well as the correctness of their calculations. Multiple competing views and uncertainties remain regarding the setup and solution of the problem.

Contextual Notes

There are unresolved aspects regarding the assumptions made in the calculations, particularly concerning the forces acting on the box and the inclusion of additional accelerations due to the car's motion.

cmcd
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The problem is stated in the attachment.

I would include my attempt at the question if I got anywhere.
I'm really only looking for a hint as to how I set up the solution.

PS, I understand how to work out the angle if the car wasn't moving.

Thanks




Homework Statement


Homework Equations


The Attempt at a Solution

 

Attachments

Physics news on Phys.org
It's question 11 by the way
 
cmcd said:
The problem is stated in the attachment.

I would include my attempt at the question if I got anywhere.
I'm really only looking for a hint as to how I set up the solution.

PS, I understand how to work out the angle if the car wasn't moving.

Thanks




Homework Statement


Homework Equations


The Attempt at a Solution


Start with a free body diagram (FBD).
 
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Is the radius of curvature and the speed of the car of any relevance?
 
At first glance, I don't think so. Your FBD will include forces, which will sum and be related to the acceleration...
 
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So I don't think I did it correct. I got an answer of 10.873°.

I started off with the forces on the box being mgsinθ parallel down the plain and mgcosθ perpendicular into the plain.

I broke up m x 4 (... mass x acceleration) into two components, 4mcosθ acting parallel to and up the plain, and 4msinθ acting into the plain.

Angle for slip...

mgsinθ + (mgcosθ + masinθ) x μ = macosθ

(g+μa)sinθ = (a - μg)cosθ

θ = ArcTan [(a-μg)/(g+μa)]

θ = 10.87°
 
cmcd said:
So I don't think I did it correct. I got an answer of 10.873°.

I started off with the forces on the box being mgsinθ parallel down the plain and mgcosθ perpendicular into the plain.

I broke up m x 4 (... mass x acceleration) into two components, 4mcosθ acting parallel to and up the plain, and 4msinθ acting into the plain.

Angle for slip...

mgsinθ + (mgcosθ + masinθ) x μ = macosθ

(g+μa)sinθ = (a - μg)cosθ

θ = ArcTan [(a-μg)/(g+μa)]

θ = 10.87°

Could you attach your FBD? That would be a help in figuring this out...
 
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http://s1372.photobucket.com/user/cmcdona22/library/?sort=3&page=1

Thanks
 
cmcd said:
Is the radius of curvature and the speed of the car of any relevance?

berkeman said:
At first glance, I don't think so. Your FBD will include forces, which will sum and be related to the acceleration...

Sorry, maybe I confused you with my reply. The motion of the car on the curved surface adds an additional acceleration beyond just gravity. That term should also be added in.
 
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  • #10
Is that an additional tangential and normal acceleration?
 
  • #11
cmcd said:
Is that an additional tangential and normal acceleration?

The braking force would be tangential and the centripetal force would be normal, right?
 
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  • #12
Hey Berkeman, does this look okay to you?
I followed it through and I got an answer of 3.8° which is isn't right, but I think the FBD looks okay.
Thanks,
cmcd
 

Attachments

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