A Banked Turn With Friction- min and max velocity

[mmoadi]

Homework Statement

A car drives through a turn with a bank angled at 25º according to horizontal floor. How much does the highest speed of the car have to be to prevent the car from slipping on the slope upwards? How much does the smallest speed of the car have to be to prevent the car from slipping on the slope downwards? Radius of the turn is 50m and the coefficient of static friction is 0, 35.

Homework Equations

F= mg
f= µN
F_centripetial= mv² / r

The Attempt at a Solution

For the max speed (v_max) that you can safely use for car to not slip up:

F_net= Nsinθ + fcosθ= (tanθ+µ / 1-tanθ)mg

F_net = F_centripetal
v_max= sqrt((tanθ+µ / 1-tanθ)rg)= 21.6 m/s

For the min speed (v_min) that you can safely use for car not to slip down:

F_net= Nsinθ - fcosθ= (tanθ-µ / 1-tanθ)mg

F_net = F_centripetal
v_max= sqrt((tanθ-µ / 1-tanθ)rg)= 8.25 m/s

Are my calculations correct?

 

[ehild]

Show your derivation a bit more detailed. Your formulas are not correct now. What do you mean on

(tanθ+µ / 1-tanθ) ? tanθ cancels.

ehild
ehild

 

[mmoadi]

I would really like to know if my approach resolving this problem is correct?
thank you!