Question

Help please I don't no how to do these

The curved section of a horizontal highway is a circular unbanked areof radius 760 m. If the coefficient of statiefriction between this roadway and typical tires is 0.40m, what would be the maximum safe driving speed for this horizontal curved section of highway? When a car goes around a banked circular curve at the proper speed for the banking angle, what force cause it to follow the circular path? gravity the friction force from the road the normal force from the road No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration. A particularly scary roller coaster contains a loop-the-Ioop in which the car and rider are completely upside down. If the radius of the loop is 15 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.

Answer 1

8) Friction force = centripetal force

umg = mv^2/r =========> v = sqrt(urg) = sqrt(0.4*760*9.8) = 54.58 m/s

9) the normal force from the road

10) Centripetal acceleration around a circle is a = v^2/R.
In the case of the loop, the acceleration must at least equal the acceleration due to gravity - at the top of the loop the centripetal acceleration is pointing up, gravity is pointing dowm, and the if gravity is greater then the net acceleration is down and away from the seat:
g = v^2/R
v = sqrt(gR) = sqrt(9.81 m/s^2 * 15m) = 12.13 m/s

So at v= 12.13 m/s the rider hits "freefall", and at greater speeds actually still feels pressed into their seat.