---
title: "A neighbor’s child wants to go to a carnival to experience the wild rides. The neighbor is worried about safety because one of the rides looks particularly dangerous. She knows that you have taken physics and so asks you for advice. The ride in question has a \\(4 \\, \\text{kg}\\) chair which hangs freely from a \\(10 \\, \\text{m}\\) long chain attached to a pivot on the top of a tall tower. When the child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up, the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed, which corresponds to one rotation about the tower every \\(3 \\, \\text{seconds}\\). When you ask the operator, he says the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds, and he weighs \\(90 \\, \\text{kg}\\)."
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url: "https://nerd-notes.com/ubq/21481/"
date_modified: "2026-05-04T07:26:37+00:00"
---

# A neighbor’s child wants to go to a carnival to experience the wild rides. The neighbor is worried about safety because one of the rides looks particularly dangerous. She knows that you have taken physics and so asks you for advice. The ride in question has a \(4 \, \text{kg}\) chair which hangs freely from a \(10 \, \text{m}\) long chain attached to a pivot on the top of a tall tower. When the child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up, the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed, which corresponds to one rotation about the tower every \(3 \, \text{seconds}\). When you ask the operator, he says the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds, and he weighs \(90 \, \text{kg}\).

A neighbor’s child wants to go to a carnival to experience the wild rides. The neighbor is worried about safety because one of the rides looks particularly dangerous. She knows that you have taken physics and so asks you for advice. The ride in question has a \(4 \, \text{kg}\) chair which hangs freely from a \(10 \, \text{m}\) long chain attached to a pivot on the top of a tall tower. When the child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up, the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed, which corresponds to one rotation about the tower every \(3 \, \text{seconds}\). When you ask the operator, he says the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds, and he weighs \(90 \, \text{kg}\).

![A physical setup diagram showing a tall vertical tower with a pivot point at the top. A single chain of length 10 meters hangs from the pivot, connected to a chair. The chair and chain are drawn at an angle theta from the vertical. The child is depicted as a simplified block sitting in the chair. A dashed circular path is drawn indicating the radius of rotation of the chair. A horizontal dimension line indicates the radius r, and an arc marker labels the angle theta between the vertical tower and the taut chain.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-21481-1777879449-kskkHF.jpg)

**Part a)** Has the operator shown that the ride is safe for a \(25 \, \text{kg}\) child? *(2 points)*

**Part b)** Using equations, support your argument and show why it aligns with your response from part (a). *(5 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/21481/*