- #1

AHinkle

- 18

- 0

## Homework Statement

## Homework Equations

[tex]\Sigma[/tex]F=ma

a

_{c}=(v^2/r)

f = [tex]\mu[/tex]N

## The Attempt at a Solution

[tex]\Sigma[/tex]F

_{radial}= (radial-coordinate of normal force) + (radial component of friction) = ((mass)(velocity^2)/(radius))

[tex]\Sigma[/tex]F

_{y}= (y-component of normal force) - (y-component of friction) = (mass)(gravity)

[tex]\Sigma[/tex]F

_{radial}= Nsin[tex]\theta[/tex]+[tex]\mu[/tex]Ncos[tex]\theta[/tex] = (mv^2/r)

[tex]\Sigma[/tex]F

_{y}=Ncos[tex]\theta[/tex] - [tex]\mu[/tex]Nsin[tex]\theta[/tex] = (mg)

I divided the equations for F

_{radial}by the equation for F

_{y}

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

V

_{max}= 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: