- #1
bornofflame
- 56
- 3
Homework Statement
The coefficient of static friction between a tire and a dry road is about μs=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 ≤ μsN
fmax = μs-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 = may = 0, so: N = mg
x: f = max = μN = μmg, so: ax = μg
amax = μg = (0.85)(9.8m/s2) = 8.33m/s2
b. r = 110m, Vmax = ?
a⊥ = V2 / r, so: V2 = a⊥r, and V = ±√(a⊥r),
which means:
Vmax = ±√(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 Fmax which I am assuming is friction max because that is the only force at work keeping the vehicle from sliding off the road.