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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 = 60.0 m above the ground and slides along a frictionless track. The car encounters a loop of radius R = 20.0 m at ground level, as shown. As you will learn in the course of this problem, the initial height 60.0 m is great enough so that the car never loses contact with the track. Find the kinetic energy K of the car at the top of the loop. 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.

Answer :

The answer is 9800 J = + K.

Solution:

For this we can use energy conservation, the block starts at h=60 m, and at the top of the loop it is at h=2 x 20 = 40 m

Then:

E1 = E2

[tex]mgh_1=mgh_2+K[/tex]

[tex]mgh_1=mgh_2=+K[/tex]

[tex]50\cdot 9.8(60-40)=+K[/tex]

[tex]9800\, J=+K[/tex]

The min-height property defines the minimum height of the element. If the content is less than the minimum height, the minimum height is applied. Minimum Height means the vertical distance measured from the slope as defined herein to the lower limit of the sign or sign structure. Sample 1 Sample. Minimum height means the minimum building height permitted on a property or part of a property.

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