Max angle for parking on a steep hill with coefficient of friction 0.8

[dabouncerx24]

The coefficient of friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (max angle) can you leave a car parked?


I have no idea how to do it since it doesn't give you the weight or anything.

 

[Pyrrhus]

Let's see, so why don't you assign the car a mass m, and then start doing the forces analysis, and see what will be the force of friction be, and you know the force of gravity (a component of it) will be the force making the car fall, so if the friction force equals that force they will cancel and the car won't fall, then you can find the angle for that case.

 

[dabouncerx24]

Forces analysis..meaning the Friction Force = Ums + Fn equation??
The component of force of gravity will simply be Fwsin? right.


I am so bad in physics...

 

[Pyrrhus]

Well on

y-axis:

$$N = mgcos\theta$$

on x-axis:

If there's not movement
$$-mgsin\theta + \mu_{s}mgcos\theta = 0$$

if

$$\mu_{s}mgcos\theta = mgsin\theta$$

Then the block should be at equilibrium, and the angle theta should be the max angle.

solve for theta (i simplifyed for you, and remember your trigonometry)

$$\mu_{s}cos\theta = sin\theta$$

 

[dabouncerx24]

thank you very much

 

[Pyrrhus]

Welcome to PF!, it was a pleasure to be of assistance, also don't discourage yourself on physics, the universe we live is a very interesting place, where many theories tries to explain how it works. Just imagine the problems, understand the concepts... and you should do ok

 

[dabouncerx24]

I'm sure I will get better as time progress, thank you for the warm welcome for I am sure I will be coming here A LOT during the school year.

Well...another problem already.

A car can decelerate at -5.10 m/s^2 w/o skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 12 degrees upward.

I'm guessing the sigma F equation comes into play here...? Thats all I know...

 

[Pyrrhus]

i'm sorry, I'm spanish what's skidding?

 

[TenaliRaman]

Cyclovenom,
skidding means sliding on a surface ...

dabouncer,
for the first case of level road,
what parameters can u find out ? (note : the car comes to rest)
whatever parameters u find for this case , apply it to second case and find its deceleration? ...

-- AI