Determine max force and acceleration to safely make a turn

[bornofflame]

Homework Statement

The coefficient of static friction between a tire and a dry road is about μ_s=0.85. What is the fastest you can safely drive the turn below?
a. Use a free-body diagram and force equations to determine the maximum force and acceleration you can achieve.
b. Use the map to estimate the radius and maximum velocity of the turn.

I don't have the map readily available but the radius is estimated at approximately 110m.

Homework Equations

F = ma
f ≤ μ_sN
f_max = μ_s-maxN
W = mg
a_⊥ = V²/r

The Attempt at a Solution

a[/B].

I drew my force diagrams and got the following (repeated from image):
y: N - mg = ma_y = 0, so: N = mg
x: f = ma_x = μN = μmg, so: a_x = μg

a_max = μg = (0.85)(9.8m/s²) = 8.33m/s²

b. r = 110m, V_max = ?
a_⊥ = V² / r, so: V² = a_⊥r, and V = ±√(a_⊥r),
which means:
V_max = ±√(a_⊥-maxr) = ±√(8.33m/s²⋅110m)=±30.3m/s
I'm satisfied with my answer for part b, but am including it just in case there is something that is wrong with it. My main concern, however, is part a as I can't seem to figure out how to get the F_max which I am assuming is friction max because that is the only force at work keeping the vehicle from sliding off the road.

 

[kuruman]

If you know a_max and you know that F_net = ma, what do you think F_{net, max} might be?
Also, I would drop the ± signs. You are calculating magnitudes of vectors here.

 

[TSny]

If you aren't given the mass of the vehicle, then I don't think you can get a numerical value for the force.

 

[kuruman]

If you aren't given the mass of the vehicle, then I don't think you can get the force.

Oops, I didn't notice that it's not given.

 

[bornofflame]

Also, I would drop the ± signs. You are calculating magnitudes of vectors here.

Ok. I'll keep that in mind. I was thinking to keep it b/c I was thinking of velocity as a vector, but it's definitely asking what is the fastest. Thanks for pointing that out.

If you aren't given the mass of the vehicle, then I don't think you can get a numerical value for the force.

Yeah. Unfortunately no mass which is what's blocking me.

 

[haruspex]

Unfortunately no mass which is what's blocking me.

I'm not sure it wants a numerical value for that. The way it is worded, it could just be telling you the steps to go through to find the speed.

 

[bornofflame]

I'm not sure it wants a numerical value for that. The way it is worded, it could just be telling you the steps to go through to find the speed.

Okay. I wasn't sure that there was a way to replace mass that I just wasn't seeing. I'll follow up with my professor. Thanks.