Question

A car speeds over a hill past point A, as shown in the figure. What is the maximum speed the car can have at point A such that its tires will not leave the track? Round to one decimal place and include units. Image:

Answer 1

11.8 m/s

Step-by-step explanation:

At the top of the hill, there are two forces on the car: weight force pulling down (towards the center of the circle), and normal force pushing up (away from the center of the circle).

Sum of forces in the centripetal direction:

∑F = ma

mg − N = m v²/r

At the maximum speed, the normal force is 0.

mg = m v²/r

g = v²/r

v = √(gr)

v = √(9.8 m/s² × 14.2 m)

v = 11.8 m/s