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.

PART A:

Find the kinetic energy K 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.

Explanation / Answer

Here ,

h = 48 m

part A)

let the kinetic energy of the car at top of the loop is KE

using conservation of energy

KE = m * g * (h - 2R)

KE = 50 * 9.8 * (48 - 2 * 16)

KE = 7840 J

the kinetic energy K of the car at the top of the loop is 7840 J

B) for the velocity at the top is v

for the box to stay in contact

v^2/16 = 9.8

v = 12.52 m/s

( hmin - 2 * 16) * 50 * 9.8 = m * v^2 0.5

hmin - 32 = 12.52^2/(2 * 9.8)

hmin = 40 m

the minimum height at which the car can stay is 40 m

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