Force of an unbanked curve

Question

a.) A 3800 kg car is traveling around an unbanked corner (horizontal road) at the recommended speed of 65 km h^-1. The radius of the curve is 80 m. What is the force that the road exerts on the car to keep it in motion around the corner?

b.) What force would the road need to exert of the car was travelling at 100 km h^-1?

Answer 1

Centripetal force is the the force required to put an object into constant circular motion. "constant circular motion" means constant tangential velocity and therefor constant angular acceleration, which is v^2 / r.

So, F=m*a = mv^2 / r

Watch out for units!! These formulas are typically in the MKS system, meaning "Meters, Kilograms, Seconds"

So, we need the speed in m/sec:

65 km/hr * 1hr/3600sec * 1000m/km = 65/3.6 m/sec

So......F = mv^2 / r = 3800 * (65/3.6)^2 / 80