---
title: "A small block of negligible dimensions slides without friction along a track that includes a vertical circular loop of radius \\(R = 1.10 \\text{ m}\\). The minimum speed of the block at the top of the loop to maintain contact with the track is \\(3.3 \\text{ m/s}\\). The block is replaced by a bowling ball modeled as a uniform solid sphere of mass \\(M = 5.0 \\text{ kg}\\) and radius \\(r = 0.10 \\text{ m}\\) that rolls without slipping along the track. What is the minimum speed of the center of mass of the bowling ball at the top of the loop such that the ball maintains contact with the track?"
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url: "https://nerd-notes.com/ubq/124479/"
date_modified: "2026-09-28T14:06:05+00:00"
---

# A small block of negligible dimensions slides without friction along a track that includes a vertical circular loop of radius \(R = 1.10 \text{ m}\). The minimum speed of the block at the top of the loop to maintain contact with the track is \(3.3 \text{ m/s}\). The block is replaced by a bowling ball modeled as a uniform solid sphere of mass \(M = 5.0 \text{ kg}\) and radius \(r = 0.10 \text{ m}\) that rolls without slipping along the track. What is the minimum speed of the center of mass of the bowling ball at the top of the loop such that the ball maintains contact with the track?

A small block of negligible dimensions slides without friction along a track that includes a vertical circular loop of radius \(R = 1.10 \text{ m}\). The minimum speed of the block at the top of the loop to maintain contact with the track is \(3.3 \text{ m/s}\). The block is replaced by a bowling ball modeled as a uniform solid sphere of mass \(M = 5.0 \text{ kg}\) and radius \(r = 0.10 \text{ m}\) that rolls without slipping along the track. What is the minimum speed of the center of mass of the bowling ball at the top of the loop such that the ball maintains contact with the track?

![A vertical circular loop of a track is shown in cross section. At the bottom, a horizontal track line extends to the left, tangent to the loop. At the apex of the loop, on the inner surface of the track, sits a shaded circular disk representing a sphere. A dashed line extends from the center of the circular loop upward to the topmost point of the track's inner surface, labeled with a dimension arrow and the text \(R\). The sphere at the apex has a solid dot at its center, with a straight radial arrow extending from its center to its outer surface labeled \(r\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604365-8ZI05D.jpg)

- **A.** \(2.6 \text{ m/s}\)
- **B.** \(2.8 \text{ m/s}\)
- **C.** \(3.1 \text{ m/s}\)
- **D.** \(3.3 \text{ m/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124479/*