A car rounds a banked curve where the radius of curvature of the road is R, the banking angle is , and the coe

Question

A car rounds a banked curve where the radius of curvature of the road is R, the banking angle is , and the coefficient of static friction is µ.

(a) Determine the range of speeds the car can have without slipping up or down the road. (Use mu for µ, theta for , and R and g as appropriate in your equations.)

minimum speed _________
maximum speed __________


(b) What is the range of speeds possible if R = 110 m, = 10°, and µ = 0.14 (slippery conditions)?
minimum speed _________m/s
maximum speed _________m/s

Answer 1

Look at a FBD for the car if it will slip down the incline

v=speed of the car


m*g*sin(th)-m*v^2/R*cos(th)
<(m*g*cos(th)+m*v^2/R*sin(th))*µ

g*sin(th)-v^2/R*cos(th)
<(g*cos(th)+v^2/R*sin(th))*µ

for slipping up the slope

m*v^2/R*cos(th)-m*g*sin(th)
<(m*g*cos(th)+m*v^2/R*sin(th))*µ

v^2/R*cos(th)-g*sin(th)
<(g*cos(th)+v^2/R*sin(th))*µ

Do the algebra and you'll have v

b)
6.18

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