# Maximum speed of car round banked bend

1. Jan 24, 2008

1. The problem statement, all variables and given/known data
Car mass m drives round a bend in a circular arc radius 44m with the road banked at an angle $$\alpha$$ where tan$$\alpha$$=3/4. The coefficient of friction $$\mu$$=0.6 of the car with the road. What is the maximum velocity the car can travel at without sliding up the banked road?

2. Relevant equations
F=ma F=mv^2/r Friction(max)=$$\mu$$r
3^2 + 4^2= 5^2

3. The attempt at a solution
The normal reaction force R perpendicular to the bank will be mgcos$$\alpha$$
R=0.8mg

Component of R towards teh center of horizontal circle = R/sin$$\alpha$$ = mg4/3

mv^2/r= 0.6x0.8mgxcos$$\alpha$$ + mg4/3
v^2/44=0.384g +g4/3
V=27.2m/s

I've always struggled with this type of question due to taking the wrong components for reaction forces etc so would greatly appreciate any help to see if this is right.

cheers

2. Jan 24, 2008

### Shooting Star

Take the components of the forces along and normal to the slope. It'll seem easier. Draw the freebody diagram. At the maximum speed, the static frcition force along the slope is max.

(Don't plug in numbers to make it messy -- use symbols.)

3. Jan 24, 2008

Yeah i know...this was actually in a test i did this morning so i did draw out everything. Basically this was the answer i did in the test and I still stand by after working through it again but was just wanting to see if it was actually right

4. Jan 24, 2008

### Shooting Star

After simplification,

v^2/r
= g[sin(theta) + kcos(theta)]/[cos(theta) - ksin(theta)]
= g[tan(theta) + k]/[1 - ktan(theta)],

which gives me v = 32.5 m/s.

(Sorry...)

Last edited: Jan 25, 2008
5. Jan 24, 2008