Question

A âsleeping policemanâ is a bump placed in the road to restrict the speed of cars. What radius of curvature should the bump have to cause cars traveling faster than 40 km/hr to leave the ground?

Answer 1

To solve this problem, the concepts related to the balance of forces must be applied. In this case the two forces that must be in balance are the Weight and the centripetal force. Both forces are derived from Newton's second law, one of the linear movement and the other of the angular movement. The centripetal force is given by the function

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

Here,

m = mass

v =Velocity

R = Radius

And the force product of the weight is given under the function

$F_w =mg$

Here,

m = Mass

g = Gravity

As both forces are in balance we will have

$\sum F =0$

$F_w - F_c = 0$

$F_w = F_c$

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

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

Speed would be

$V = 40km/h (\frac{1000m}{1km})(\frac{1h}{3600s})$

$V = 11.11m/s$

Replacing

$R = \frac{11.11^2}{9.8}$

$R = 12.59m$

The radius must be 12.6m