Question

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?

Answer 1

Step-by-step explanation:

Given

Velocity of traffic
`v=60\ mi/hr\approx 26.82\ m/s`

Maximum value of Centripetal force is one-tenth of weight

such that
`(F_c)_(max)=(mg)/(10)`

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

`F_c=(mv^2)/(r)`

`(F_c)_(max)=(mg)/(10)=F_c=(mv^2)/(r)`

`(mg)/(10)=(mv^2)/(r)`

`r=(10v^2)/(g)`

`r=(10* 26.82^2)/(9.8)`

`r=733.99\approx 734\ m`