1. **State the problem:** A car of mass $m = 800$ kg moves around a circular track of radius $r = 50$ m at a speed $v = 10$ m/s. Find the required centripetal force $F_c$. 2. **Recall the formula for centripetal force:** The centripetal force needed to keep the car moving in a circle is given by $$F_c = \frac{m v^2}{r}$$ 3. **Plug in the values:** $$F_c = \frac{800 \times 10^2}{50}$$ 4. **Calculate the numerator:** $$800 \times 10^2 = 800 \times 100 = 80000$$ 5. **Divide by the radius:** $$F_c = \frac{80000}{50} = 1600$$ 6. **Interpretation:** The required centripetal force is $1600$ newtons. **Final answer:** $F_c = 1600$ N, which matches the second choice.