---
title: "A small cart is released from rest at height \\(h\\) on a frictionless track that leads into a vertical circular loop of radius \\(R = 1.2\\text{ m}\\). To maintain contact with the track at the highest point of the loop, the cart must have a minimum speed of \\(v_{\\text{top}} = \\sqrt{gR}\\). What is the minimum release height \\(h\\) required for the cart to complete the loop?"
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url: "https://nerd-notes.com/ubq/120660/"
date_modified: "2026-08-23T04:42:31+00:00"
---

# A small cart is released from rest at height \(h\) on a frictionless track that leads into a vertical circular loop of radius \(R = 1.2\text{ m}\). To maintain contact with the track at the highest point of the loop, the cart must have a minimum speed of \(v_{\text{top}} = \sqrt{gR}\). What is the minimum release height \(h\) required for the cart to complete the loop?

A small cart is released from rest at height \(h\) on a frictionless track that leads into a vertical circular loop of radius \(R = 1.2\text{ m}\). To maintain contact with the track at the highest point of the loop, the cart must have a minimum speed of \(v_{\text{top}} = \sqrt{gR}\). What is the minimum release height \(h\) required for the cart to complete the loop?

![A side-view diagram of a track consisting of a curved ramp on the left that transitions smoothly into a vertical circular loop of radius \(R\) on the right. A small rectangular cart sits on the ramp at a vertical height \(h\) above the flat horizontal ground. A vertical dashed dimension line labeled \(h\) extends from the ground to the cart. The circular loop rests on the ground with its center marked by a dot, and a dashed line with an arrow extends from the center to the track labeled \(R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460150-pVXKyr.jpg)

- **A.** \(1.2\text{ m}\)
- **B.** \(1.8\text{ m}\)
- **C.** \(2.4\text{ m}\)
- **D.** \(3.0\text{ m}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120660/*