---
title: "A linear spring of negligible mass requires a force of \\( 18.0 \\, \\text{N} \\) to cause its length to increase by \\( 1.0 \\, \\text{cm} \\). A sphere of mass \\( 75.0 \\, \\text{g} \\) is then attached to one end of the spring. The distance between the center of the sphere \\( M \\) and the other end \\( P \\) of the un-stretched spring is \\( 25.0 \\, \\text{cm} \\). Then the sphere begins rotating at constant speed in a horizontal circle around the center \\( P \\). The distance \\( P \\) and \\( M \\) increases to \\( 26.5 \\, \\text{cm} \\)."
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url: "https://nerd-notes.com/ubq/23323/"
date_modified: "2025-09-23T04:47:00+00:00"
---

# A linear spring of negligible mass requires a force of \( 18.0 \, \text{N} \) to cause its length to increase by \( 1.0 \, \text{cm} \). A sphere of mass \( 75.0 \, \text{g} \) is then attached to one end of the spring. The distance between the center of the sphere \( M \) and the other end \( P \) of the un-stretched spring is \( 25.0 \, \text{cm} \). Then the sphere begins rotating at constant speed in a horizontal circle around the center \( P \). The distance \( P \) and \( M \) increases to \( 26.5 \, \text{cm} \).

A linear spring of negligible mass requires a force of \( 18.0 \, \text{N} \) to cause its length to increase by \( 1.0 \, \text{cm} \). A sphere of mass \( 75.0 \, \text{g} \) is then attached to one end of the spring. The distance between the center of the sphere \( M \) and the other end \( P \) of the un-stretched spring is \( 25.0 \, \text{cm} \). Then the sphere begins rotating at constant speed in a horizontal circle around the center \( P \). The distance \( P \) and \( M \) increases to \( 26.5 \, \text{cm} \).

**Part a)** Explain why the spring increases in length when the sphere is moving in a circle. *(3 points)*

**Part b)** Determine the speed of the sphere. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/23323/*