In the Daytona 500 car race in Daytona, FL, a curve in the oval track has a radius of 316 m (near

Question

the top of the curve) and is banked at 31.0
O
.
a) What speed would be necessary to make this turn if there was no friction on the road?
b) If the coefficient of static friction between the tires and the road is 0.70, what are the minimum
and maximum speeds that a car could take this turn and not slide?

Answer 1

(a)
x: ma=N•sinα
y: 0=N•cosα –mg, => N=mg/cosα
a=v²/R
m• v²/R = N•sinα= mg•sinα/cosα= mg•tanα
v=sqrt(R• g•tanα)
(b)
x: ma=N•sinα+F(fr) •cosα
y: mg= N•cosα –mg-F(fr) •sinα

Since F(fr)=μ•N,
ma=N(sinα+μ•cosα)
mg= N(cosα - μ• sinα)
ma/mg = (sinα+μ•cosα)/ (cosα - μ• sinα)
a=v² /R
v² /Rg= (sinα+μ•cosα)/ (cosα - μ• sinα)
v=sqrt[Rg (sinα+μ•cosα)/ (cosα - μ• sinα)]