Cushion seat angle : Radius of curvature

[cmcd]

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

 

[cmcd]

It's question 11 by the way

 

[berkeman]

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).

 

[cmcd]

Is the radius of curvature and the speed of the car of any relevance?

 

[berkeman]

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

 

[cmcd]

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]

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...

 

[cmcd]

http://s1372.photobucket.com/user/cmcdona22/library/?sort=3&page=1

Thanks

 

[berkeman]

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.

 

[cmcd]

Is that an additional tangential and normal acceleration?

 

[berkeman]

Is that an additional tangential and normal acceleration?

The braking force would be tangential and the centripetal force would be normal, right?

 

[cmcd]

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