Question

If this speed is based on what would be safe in wet weather, estimate the radius of curvature for a curve marked 70 km/h . The coefficient of static friction of rubber on wet concrete is μs=0.7, the coefficient of kinetic friction of rubber on wet concrete is μk=0.5

Answer 1

as it is given that curved marked the speed as v = 70 km/h

so we will first convert the speed into m/s

`v = 70 km/h = 19.44 m/s`

now we know that here friction force will provide centripetal force

`F_c = F_f`

As we know that centripetal force is given as

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

`(mv^2)/(R) = \mu_k mg`

`(v^2)/(R) = \mu_k g`

`v^2 = \mu_k R * g`

`19.44^2 = 0.5* R * 9.8`

`378 = 4.9 * R`

`R = 77.1 m`

Answer 2

54.86 m

Step-by-step explanation:

The radius of curvature for a curve marked can be calculated by equating centripetal force and force of frcition.

`(mv^2)/(r)=\mu mg\\ \Rightarrow (v^2)/(r) = \mu g\\ \Rightarrow r = (v^2)/(\mu g)`

v = 70 km/h = 19.4 m/s

Substitute the values:

`r = ((19.4 m/s)^2)/((0.7) (9.8m/s^2))=54.86 m`