A car in an amusement park ride travels without friction along the track shown i

Question

A car in an amusement park ride travels without friction along the track shown in the accompanying figure, starting from rest at point A.(Figure 1)

FIGURE 1: http://session.masteringphysics.com/problemAsset/1342983/2/1027496.jpg

Part A
If the loop the car is currently on has a radius of 22.0{ m m} , find the minimum height h so that the car will not fall off the track at the top of the circular part of the loop.
h = ______________{ m m}

Explanation / Answer

Potential energy ( m . g . h ) must give the KE that the car needs PLUS the GPE the car needs to go over the top of the loop ->GPE needed is m . g . 2R = 44 . m . g ->KE = mv^2 / R = mg mv^2 / 2 = mgR / 2 =>total energy needed = 44mg + 11 mg = 55 mg =>Starting height needed = 55 m

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