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Cushion seat angle : Radius of curvature

  • Thread starter cmcd
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  • #1
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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

 

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Answers and Replies

  • #2
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It's question 11 by the way
 
  • #3
berkeman
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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

Start with a free body diagram (FBD).
 
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  • #4
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Is the radius of curvature and the speed of the car of any relevance?
 
  • #5
berkeman
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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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  • #6
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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°
 
  • #7
berkeman
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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°
Could you attach your FBD? That would be a help in figuring this out...
 
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  • #9
berkeman
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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...
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
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Is that an additional tangential and normal acceleration?
 
  • #11
berkeman
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Is that an additional tangential and normal acceleration?
The braking force would be tangential and the centripital force would be normal, right?
 
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  • #12
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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
 

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