# Thread: Newton's second law and centripetal forces

1. ## Newton's second law and centripetal forces

Fifteen clowns are late to a party. They jump into their sporty coupe and start driving. Eventually they come to a level curve, with a radius of 31.5 meters. What is the top speed at which they can drive successfully around the curve? The coefficient of static friction between the car's tires and the road is 0.800.

2. Originally Posted by Linnus
Fifteen clowns are late to a party. They jump into their sporty coupe and start driving. Eventually they come to a level curve, with a radius of 31.5 meters. What is the top speed at which they can drive successfully around the curve? The coefficient of static friction between the car's tires and the road is 0.800.
The latteral acceleration on a curve of radius $\displaystyle r$ at speed $\displaystyle v$ is:

$\displaystyle a_{lat}=\frac{v^2}{r}$

This must be matched by the lateral tire friction, and this has a maximum before onset to skid of

$\displaystyle F_{max}=mg\mu$

where $\displaystyle \mu$ is the coefficient of static friction.

So the maximum speed aroud a curve of radius $\displaystyle r$ satisfies:

$\displaystyle \frac{v^2}{r}=g \mu$

ZB