Question

You are driving a 2500.0-kg car at a constant speed of 13.0 m/s along an icy, but straight and level road. While approaching a traffic light, it turns red. You slam on the brakes, Your wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 25.0 m. What is the coefficient of sliding friction (µ) between your tires and the icy roadbed?

Answer 1

Given:

$$m = 2500 \text{ kg}$$ $$v_1 = 14 \quad \text{m/s}$$ $$d = 25 \text{ m}$$

Need to find: $\mu - ?$

Solving:

$$F_t = F_N = ma \Rightarrow$$ $$\Rightarrow -\mu mg = \frac{m(v_t^2 - v_1^2)}{2d}, \text{ where } v_t = 0.$$

So, we will have:

$$-\frac{m(v_t^2 - v_1^2)}{2d} = \mu mg \Rightarrow$$ $$\Rightarrow -\frac{(v_t^2 - v_1^2)}{2d} = \mu g \Rightarrow \mu = -\frac{(v_t^2 - v_1^2)}{2gd} = \frac{v_1^2}{2gd} = \frac{14^2}{2 \cdot 9.8 \cdot 25} = \frac{196}{490} = 0.4.$$

Answer: 0.4.