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A roller-coaster car may be represented by a block of mass 50.0 kg. The car is released from rest at a height h = 48.0 m above the ground and slides along a frictionless track. The car encounters a loop of radius R = 16.0 m at ground level, as shown. As you will learn in the course of this problem, the initial height 48.0 m is great enough so that the car never loses contact with the track .
Part A
Find the kinetic energy
of the car at the top of the loop.
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of the car at the top of the loop.Express your answer numerically, in joules.
Part B
Find the minimum initial height hmin at which the car can be released that still allows the car to stay in contact with the track at the top of the loop.
Express your answer numerically, in meters.
♦ Relevant knowledge
According to the law of conservation energy, energy cannot be created or destroyed. It can only be transformed from one form to the other. A body can possess kinetic energy by virtue of its motion. We need to provide kinetic energy to a body that needs to move. A momentum exchange occurs when two bodies collide. The square root of kinetic energie is the direct measure of how much momentum there is.
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