Question

On a highway curve with a radius of 46 meters, the maximum force of static friction that can act on a 1,200 kg car going around the curve is 7,500 Newtons. What speed limit should be posted for the curve so that cars can negotiate it safely

Answer 1

`v\approx 16.956\,(m)/(s)`

Step-by-step explanation:

The motion of the vehicule on a highway curve can be modelled by the following equation of equilibrium:

`\Sigma F = f = m\cdot (v^(2))/(R)`

The maximum speed is:

`v = \sqrt{(f\cdot R)/(m) }`

`v = \sqrt{((7500\,N)\cdot (46\,m))/(1200\,kg) }`

`v\approx 16.956\,(m)/(s)`