# Problem: 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 = 54.0m above the ground and slides along a frictionless track. The car encounters a loop of radius R = 18.0m at ground level, as shown. As you will learn in the course of this problem, the initial height 54.0m is great enough so that the car never loses contact with the track.A. Find an expression for the kinetic energy K of the car at the top of the loop.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.

🤓 Based on our data, we think this question is relevant for Professor Cooney's class at UCF.

###### FREE Expert Solution

The centripetal force:

$\overline{){{\mathbf{F}}}_{{\mathbf{C}}}{\mathbf{=}}\frac{\mathbf{m}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}}$

A.

The potential energy is converted to kinetic energy as:

K.E = mgh'

h' in this case is h - 2R

###### Problem Details

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 = 54.0m above the ground and slides along a frictionless track. The car encounters a loop of radius R = 18.0m at ground level, as shown. As you will learn in the course of this problem, the initial height 54.0m is great enough so that the car never loses contact with the track.

A. Find an expression for the kinetic energy K of the car at the top of the loop.

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.