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title: "A block of mass \\(m\\) rests on a flat horizontal surface. Starting at time \\(t = 0\\), a constant horizontal force of magnitude \\(F_0\\) is applied to the block. The coefficient of static friction between the block and the surface decreases over time according to \\(\\mu_s(t) = \\mu_0 – bt\\), where \\(\\mu_0\\) and \\(b\\) are positive constants, and \\(F_0 < \\mu_0 mg\\). In terms of \\(m\\), \\(g\\), \\(F_0\\), \\(\\mu_0\\), and \\(b\\), at what time \\(t\\) does the block begin to slip?"
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url: "https://nerd-notes.com/ubq/117544/"
date_modified: "2026-08-04T07:48:58+00:00"
---

# A block of mass \(m\) rests on a flat horizontal surface. Starting at time \(t = 0\), a constant horizontal force of magnitude \(F_0\) is applied to the block. The coefficient of static friction between the block and the surface decreases over time according to \(\mu_s(t) = \mu_0 – bt\), where \(\mu_0\) and \(b\) are positive constants, and \(F_0 < \mu_0 mg\). In terms of \(m\), \(g\), \(F_0\), \(\mu_0\), and \(b\), at what time \(t\) does the block begin to slip?

A block of mass \(m\) rests on a flat horizontal surface. Starting at time \(t = 0\), a constant horizontal force of magnitude \(F_0\) is applied to the block. The coefficient of static friction between the block and the surface decreases over time according to \(\mu_s(t) = \mu_0 - bt\), where \(\mu_0\) and \(b\) are positive constants, and \(F_0 < \mu_0 mg\). In terms of \(m\), \(g\), \(F_0\), \(\mu_0\), and \(b\), at what time \(t\) does the block begin to slip?

- **A.** \(t = \dfrac{\mu_0 mg + F_0}{b mg}\)
- **B.** \(t = \dfrac{\mu_0 mg - F_0}{b mg}\)
- **C.** \(t = \dfrac{F_0}{b \mu_0 mg}\)
- **D.** \(t = \dfrac{F_0}{b mg}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117544/*