When do the park brakes need to be applied=f(critical inclined angle)

[marellasunny]

The coefficient of static friction is defined at the critical/Maximum inclination angle at which the block "begins" to slide. Hence, for a vehicle on an inclined plane at this critical angle, the braking force at this critical angle is given by:
i.e $$F_{braking}=\mu_{static} N$$ at $\theta _{max}$

For anything beyond$i.e >\theta_{max}$ the braking force is given as
$$F_{braking}=\mu_{dynamic} N$$

Obviously,at any angle below the critical angle, the vehicle "park brakes" need not be applied because the vehicle will not move.

My question: Will the "park brakes" need to be applied AT the critical angle or BEYOND the critical angle?

Assumption:
Both the front and rear tires are on a the road with same coefficients of friction.

 

[jbriggs444]

There is no such thing as an exact angular measurement in physics. Accordingly, there is no detectable difference between "at the critical angle" and "just beyond the critical angle".

If you want assurance that your car will not roll into the lake, apply the parking brakes.

 

[nasu]

The brakes (parking or regular) will not prevent the car sliding down the slope.
If the angle of the slope is larger than the critical angle for the given road conditions, the car will slide down even with the brakes on.
Putting the brakes prevents rolling, which will I suppose will start at a much smaller angle.
These formulas are not quite relevant for something rolling on wheels.

 

[marellasunny]

Nasu,jbriggs:
Now,the concept of the critical friction angle is more clear.Its the angle at which the object starts to slide down.
Q:Would I be right in stating that the "tire slip" (otherwise called as flex of the rubber) would be maximum just at the point of the critical angle and lessens out once the car starts sliding? <=>because the static friction acts just at the point of the critical angle and dynamic friction acts at angles BEYOND i.e since $\mu_{static}> \mu_{dynamic}$.(Am I right?)