---
title: "A \\(90 \\, \\text{kg}\\) individual is cycling up a hill inclined at \\(30^\\circ\\) on a \\(12 \\, \\text{kg}\\) bicycle. The hill is quite steep, and the coefficient of static friction is \\(0.85\\). The cyclist ascends \\(12 \\, \\text{m}\\) up the hill and then pauses at the summit. They then start descending from rest and travel \\(9 \\, \\text{m}\\) before firmly applying the brakes, causing the wheels to lock."
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url: "https://nerd-notes.com/ubq/23109/"
date_modified: "2025-10-02T13:14:19+00:00"
---

# A \(90 \, \text{kg}\) individual is cycling up a hill inclined at \(30^\circ\) on a \(12 \, \text{kg}\) bicycle. The hill is quite steep, and the coefficient of static friction is \(0.85\). The cyclist ascends \(12 \, \text{m}\) up the hill and then pauses at the summit. They then start descending from rest and travel \(9 \, \text{m}\) before firmly applying the brakes, causing the wheels to lock.

A \(90 \, \text{kg}\) individual is cycling up a hill inclined at \(30^\circ\) on a \(12 \, \text{kg}\) bicycle. The hill is quite steep, and the coefficient of static friction is \(0.85\). The cyclist ascends \(12 \, \text{m}\) up the hill and then pauses at the summit. They then start descending from rest and travel \(9 \, \text{m}\) before firmly applying the brakes, causing the wheels to lock.

**Part a)** Draw or Describe a Free Body Diagram (FBD) of the scenario. *(1 points)*

**Part b)** Calculate the amount of work performed by friction to stop the bicycle completely, given that the coefficient of kinetic friction is \(0.7\). *(4 points)*

**Part c)** Using equations explain and justify why cyclist would finds it harder to travel up the incline compared to coming down the incline. *(2 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/23109/*