A car approaches the top of a hill that is shaped like a vertical circle with ra

Question

A car approaches the top of a hill that is shaped like a vertical circle with radias, r=55.0m. What is the fastest speed a car can go over the top of the hill without loosing contact with the ground?

Explanation / Answer

mv^2/r = mg =>v = sqrt[gr] =>v = sqrt[9.8 x 55] = 23.22 m/s There is nothing "non-uniform" about this problem. You can think of the hill crest shaped like a perfect circle arc and you can think of the car moving at constant speed due to impossibly perfect cruise control just to still think of it as a uniform circular motion problem. Forces acting on a car at the top of a hill crest: Weight (m*g): downward Normal force (N): upward Acceleration is centripetal acceleration, thus equal to a = v^2/r, and thus downward toward the hill center. Newton's second law for acceleration downward: m*g - N = m*a Thus: m*g - N = m*v^2/r In the case of "loosing contact", this means that the normal force becomes zero at that instant. Thus: g = v^2/r Solve for v: v = sqrt(r*g) Data: g:=9.8 N/kg; r:=55.0 m; Result: v = 23.2 meters/second

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