How Fast Can a Car Travel on a 22° Icy Banked Curve with a 170m Radius?

[Xylitol]

A curve of radius 170 m is banked at an angle of 22°. At what speed can it be negotiated under icy conditions where friction is negligible?

Can someone explain how to get the answer for this question? Thanks

 

[andrewchang]

it concerns centripetal acceleration. did you try it at all? you need to at least show some of your work or thought processes.

 

[Xylitol]

Ok
I drew out the FBD

Fg going down
Fny going up
Fnx going to the right
Fn going at a 68 degree angle to the horizontal

Using the trig functions, I got: (not to significant figures)
Fg = 9.8 [N]
Fn = 9.8 [N]
Fnx = 3.96 [N]
Fn = 10.57 [N]

Ac = (Vc^2)/(r)
Fc = MAc = (MVc^2)/(r)

 

[lightgrav]

this is for your "1 kg" car, right?

which of these Forces is center-pointing?

 

[Xylitol]

Fnx is center pointing

The mass is not given
Apparently the masses should cancel out with teh formulas but I don't really know which ones to choose

 

[robphy]

What does Fc mean? That is to say, in your last equation, what is the meaning of Fc by itself, making no reference to the rest of the equalities on that line?

Hint: how does Fc relate to your FBD?

 

[Xylitol]

What does Fc mean? That is to say, in your last equation, what is the meaning of Fc by itself, making no reference to the rest of the equalities on that line?

Hint: how does Fc relate to your FBD?

Its going towards the center

 

[robphy]

Why does one draw a FBD in the first place?
How does it help you correctly apply Newton-II? In fact, what is the precise statement of Newton-II?

 

[Xylitol]

Why does one draw a FBD in the first place?
How does it help you correctly apply Newton-II? In fact, what is the precise statement of Newton-II?

Netforce(X/Y) = MA