A roller coaster car may be approximated by a block of mass mmm. The car, which starts from rest, is released at a heighth above the ground and slides along a frictionless track. The car encounters a loop of radius R, as shown in the figure below. Assume that the initial height h is great enough so that the car never loses contact with the track. a. Find an expression for kinetic energy of the car at the top of the loop in terms of m, g, h, and R.

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Chapter1: Units, Trigonometry. And Vectors
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A roller coaster car may be approximated by a block of mass mmm. The car, which starts from
rest, is released at a height h above the ground and slides along a frictionless track. The car
encounters a loop of radius R, as shown in the figure below. Assume that the initial height h is
great enough so that the car never loses contact with the track.
Find an expression for kinetic energy of the car at the top of the loop in terms of m, g, h,
and R.
b. Find the minimum initial height h 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 in terms of R (think of the
acceleration and normal force at the top of the loop).
Transcribed Image Text:A roller coaster car may be approximated by a block of mass mmm. The car, which starts from rest, is released at a height h above the ground and slides along a frictionless track. The car encounters a loop of radius R, as shown in the figure below. Assume that the initial height h is great enough so that the car never loses contact with the track. Find an expression for kinetic energy of the car at the top of the loop in terms of m, g, h, and R. b. Find the minimum initial height h 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 in terms of R (think of the acceleration and normal force at the top of the loop).
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