---
title: "In the figure above, the marble rolls down the track and around a loop-the-loop of radius \\( R \\). The marble has mass \\( m \\) and radius \\( r \\). What minimum height \\( h_{min} \\) must the track have for the marble to make it around the loop-the-loop without falling off? Express your answer in terms of the variables \\( R \\) and \\( r \\)."
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url: "https://nerd-notes.com/ubq/47215/"
date_modified: "2024-09-20T08:40:23+00:00"
---

# In the figure above, the marble rolls down the track and around a loop-the-loop of radius \( R \). The marble has mass \( m \) and radius \( r \). What minimum height \( h_{min} \) must the track have for the marble to make it around the loop-the-loop without falling off? Express your answer in terms of the variables \( R \) and \( r \).

In the figure above, the marble rolls down the track and around a loop-the-loop of radius \( R \). The marble has mass \( m \) and radius \( r \). What minimum height \( h_{min} \) must the track have for the marble to make it around the loop-the-loop without falling off? Express your answer in terms of the variables \( R \) and \( r \).

![Diagram](https://nerd-notes.com/wp-content/uploads/2024/09/a45697fb-08ad-414b-9ac6-6308f58250b3.webp)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/47215/*