# Cushion seat angle : Radius of curvature

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

## The Attempt at a Solution

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It's question 11 by the way

berkeman
Mentor
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

## The Attempt at a Solution

• 1 person
Is the radius of curvature and the speed of the car of any relevance?

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

• 1 person
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°

berkeman
Mentor
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...

• 1 person
berkeman
Mentor
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.

• 1 person
Is that an additional tangential and normal acceleration?

berkeman
Mentor
Is that an additional tangential and normal acceleration?
The braking force would be tangential and the centripital force would be normal, right?

• 1 person
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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