An unbanked circular highway curve on level ground makes aturn
of 90 degrees. THe highway carries traffic at 60 mi/hr, andthe
centripetal force on a vehicle is not to exceed 1/10 of itsweight.
What is the minimum length of teh curve in miles?

Respuesta :

Answer:

Explanation:

Given

Velocity of traffic [tex]v=60\ mi/hr\approx 26.82\ m/s[/tex]

Maximum value of Centripetal force is one-tenth of weight

such that [tex](F_c)_{max}=\frac{mg}{10}[/tex]

to make a safe turn centripetal force with radius of curvature r is given by

[tex]F_c=\frac{mv^2}{r}[/tex]

[tex](F_c)_{max}=\frac{mg}{10}=F_c=\frac{mv^2}{r}[/tex]

[tex]\frac{mg}{10}=\frac{mv^2}{r}[/tex]

[tex]r=\frac{10v^2}{g}[/tex]

[tex]r=\frac{10\times 26.82^2}{9.8}[/tex]

[tex]r=733.99\approx 734\ m[/tex]