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title: "A pendulum consists of a mass \\( M \\) hanging at the bottom end of a massless rod of length \\( \\ell \\), which has a frictionless pivot at its top end. A mass \\( m \\), moving as shown in Fig. 7-35 with velocity \\( v \\), impacts \\( M \\) and becomes embedded. What is the smallest value of \\( v \\) sufficient to cause the pendulum (with embedded mass \\( m \\)) to swing clear over the top of its arc?"
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url: "https://nerd-notes.com/ubq/80993/"
date_modified: "2025-11-04T18:15:16+00:00"
---

# A pendulum consists of a mass \( M \) hanging at the bottom end of a massless rod of length \( \ell \), which has a frictionless pivot at its top end. A mass \( m \), moving as shown in Fig. 7-35 with velocity \( v \), impacts \( M \) and becomes embedded. What is the smallest value of \( v \) sufficient to cause the pendulum (with embedded mass \( m \)) to swing clear over the top of its arc?

A pendulum consists of a mass \( M \) hanging at the bottom end of a **massless** rod of length \( \ell \) which has a frictionless pivot at its top end. A mass \( m \), moving with velocity \( v \), impacts \( M \) and becomes embedded. In terms of the given variables and constants, what is the smallest value of \( v \) sufficient to cause the pendulum (with embedded mass \( m \)) to swing clear over the top of its arc?

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/80993/*