- #1
AHinkle
- 18
- 0
Homework Statement
Homework Equations
[tex]\Sigma[/tex]F=ma
ac=(v^2/r)
f = [tex]\mu[/tex]N
The Attempt at a Solution
[tex]\Sigma[/tex]Fradial= (radial-coordinate of normal force) + (radial component of friction) = ((mass)(velocity^2)/(radius))
[tex]\Sigma[/tex]Fy= (y-component of normal force) - (y-component of friction) = (mass)(gravity)
[tex]\Sigma[/tex]Fradial= Nsin[tex]\theta[/tex]+[tex]\mu[/tex]Ncos[tex]\theta[/tex] = (mv^2/r)
[tex]\Sigma[/tex]Fy=Ncos[tex]\theta[/tex] - [tex]\mu[/tex]Nsin[tex]\theta[/tex] = (mg)
I divided the equations for Fradial by the equation for Fy
and it yielded...
tan[tex]\theta[/tex] = (v^2-[tex]\mu[/tex]rg)/(rg+[tex]\mu[/tex]v^2)
so in order to find theta which I am looking for
[tex]\theta[/tex]= arctan (v^2-[tex]\mu[/tex]rg)/(rg+[tex]\mu[/tex]v^2)
but I have 2 unknowns...
we know
Vmax = 100km/h which is approx 27.78 m/s
g = 9.81 m/s^2 (this is given in the problem)
r= ?
[tex]\theta[/tex] = ?
[tex]\mu[/tex]= 0.22
also I am not sure how to conceptualize the part of the problem where i need to find out what theta needs to be to keep the car from sliding in the ditch.
I feel i can find the upper limit but not the lower. I thought about subbing something in for r to find theta but I'm stumped.
Last edited: