Respuesta :
The coefficient of friction μ is defined as the quotient between the force of friction f and the normal force F_N that an object is subject to:
[tex]\mu=\frac{f}{F_N}[/tex]Since the friction is responsible for decelerating the car, use Newton's Second Law of Motion to find the magnitude of f:
[tex]f=ma[/tex]The normal force is equal to the weight of the car because the surface is horizontal:
[tex]F_N=mg[/tex]Replacing the expressions for f and F_N, the coefficient of friction becomes:
[tex]\begin{gathered} \mu=\frac{ma}{mg} \\ \\ \Rightarrow\mu=\frac{a}{g} \end{gathered}[/tex]The acceleration is the rate of change of the velocity with respect to time. Since the car decelerates from 32m/s to rest in 3.94 seconds, then:
[tex]a=\frac{32\frac{m}{s}}{3.94s}=8.1218...\frac{m}{s^2}[/tex]Replace the value of a as well as g=9.81m/s^2 to find the coefficient of friction:
[tex]\begin{gathered} \mu=\frac{a}{g}=\frac{8.1218...\frac{m}{s^2}}{9.81\frac{m}{s^2}}=0.8279... \\ \\ \therefore\mu\approx0.83 \end{gathered}[/tex]Therefore, to the nearest hundredths place, the coefficient of friction is 0.83.
