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A car drives over the top of a hill that has a radius of 50 m. What maximum speed can the car have without flying off the road at the top of the hill?
Answer: v = 22.147 m/s
r = 50 m
The forces acting on the car are the normal reaction of the ground and the force of gravity.
According to Newton’s second law, we have:
F = ma
F = N -Fg
N = mg
Fg = mg
The maximum speed will be the speed at which the car barely touches the surface, so the force of the normal reaction of the ground can be neglected: