A roller-coaster car may be represented by a block of mass 50.0 kg . The car is

Question

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.

A)

Find the kinetic energy K of the car at the top of the loop.

Express your answer numerically, in joules.

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.

Explanation / Answer

potential energy at the h = 48 m is U1 = m*h*g = 50*9.81*48 = 23544 J

potential enery at the top of the loop is U2 = m*g*h2 = 50*9.81*2*16 = 15696 J

A) kinetic energy at the top of the car is K = 23544-15696 = 7848 J

B) minimum height required is 2.5*R = 2.5*16 = 40 m

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