Answer
$7500\ lb$
Work Step by Step
Step 1. Assume $F\ (lb)$ is the force needed to keep a car from skidding on a curve.
Step 2. Assume $w\ (lb)$ is the weight of the car and $v\ (mph)$ is the speed.
Step 3. From the given conditions, we have $F=kwv^2/r$ and $3000=k(2000)(30)^2/(500)$, thus $k=\frac{5}{6}$
Step 4. For $r=800\ (ft)$, $v=60\ (mph)$, we have $F=\frac{5}{6}(2000)(60)^2/(800)=7500\ lb$
