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

Answer:

54.86 m            

Explanation:

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

$\frac{mv^2}{r}=\mu mg\\ \Rightarrow \frac{v^2}{r} = \mu g\\ \Rightarrow r = \frac{v^2}{\mu g}$

v = 70 km/h = 19.4 m/s

Substitute the values:

$r = \frac{(19.4 m/s)^2}{(0.7) (9.8m/s^2)}=54.86 m$

Answer 2

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

$F_c = \frac{mv^2}{R}$

$\frac{mv^2}{R} = \mu_k mg$

$\frac{v^2}{R} = \mu_k g$

$v^2 = \mu_k R * g$

$19.44^2 = 0.5* R * 9.8$

$378 = 4.9 * R$

$R = 77.1 m$