Chapter 12.6, Problem 53ES

If an automobile of mass m rounds a curve, then its inward vector component of acceleration $a_N\text{N}$ is caused by the frictional force F of the road. Thus, it follows from the vector form of Newton’s second law [Equation (19)] that the frictional force and the normal component of acceleration are related by the equation $\text{F}=m{a}_N\text{N}\text{.}$ Thus,

$‖\text{F}‖=mk{\left(\frac{ds}{dt}\right)}^2$

Use this result to find the magnitude of the frictional force in newtons exerted by road on a 500 kg go-cart driven at a speed of 10km/h around a circular track or radius 15m. $[Note:1\text{N}=1\text{kg}.\text{m}/{\text{s}}^{\text{2}}.]$