Car going around banked curve with no friction

[chaotiiic]

Homework Statement

a racecourse is designed with curves with a radius of 200m and a 10degree banking. What is the maximum speed a car can negotiate the curve without friction?

Homework Equations

Newtons 3 laws

The Attempt at a Solution

tanTheta = v^2/gR
tan10 = v^2/(9.8 * 200m)
v = 345 m/s^2

is this right?

 

[tiny-tim]

hi chaotiiic!

tanTheta = v^2/gR
tan10 = v^2/(9.8 * 200m)

formula looks ok

are you sure about the 345 ?

(and speed is m/s, not m/s²)

 

[chaotiiic]

hi chaotiiic!


formula looks ok

are you sure about the 345 ?

(and speed is m/s, not m/s²)

so is it 0.1763 = v^2/1960
v^2=345.6
v=18.59m/s

 

[tiny-tim]

yes!

(are you ok now, or is there anything you're still not sure about?)​

 

[chaotiiic]

yes!

(are you ok now, or is there anything you're still not sure about?)​

thankyou.
im actually still confused about everything. the only reason i was able to answer this problem is because there's a problem identical in my book to the one i asked. my teacher gives out quizzes before lectures so hopefully ill understand when i go to class later today.

 

[tiny-tim]

ok, so you don't understand the reason for the formula? …

tanTheta = v^2/gR

like almost all dynamics questions, it all boils down to good ol' Newton's second law (F = ma) …

you know the acceleration (as a function of v),

and although you know the weight, you don't know the normal force …

so you do F = ma perpendicular to the unknown (normal) force ​