---
title: "Unit 2.7 | Problem Solving – Simple Pulley Systems"
description: "Solve pulley problems quickly and easily with this guide! Video, written explanations and a simple 3 step framework to solve any problem."
featured_image: "https://nerd-notes.com/wp-content/uploads/2023/06/Atwoodpulley-system.png"
url: "https://nerd-notes.com/unit-2-7-advanced-problem-solving-pulley-systems/"
date_modified: "2023-10-12T05:45:18+00:00"
---

# Unit 2.7 | Problem Solving – Simple Pulley Systems

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This course article contains videos that can only be accessed once enrolled in the [Learn AP Physics from Scratch Course](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/ap-physics-1-course-all-materials/).

### Unit 2 Breakdown

You are on Lesson 7 of 8:

1. [Unit 2.1 | Understanding and Applying Newton’s Law in Depth](https://nerd-notes.com/unit-2-1-the-forces-that-move-us-unpacking-dynamics-in-ap-physics-1/)
2. [Unit 2.2 | Common Linear Forces, Equations, and Misconceptions](https://nerd-notes.com/unit-2-2-common-forces-in-physics/)
3. [Unit 2.3 | Drawing and Understanding Force Body Diagrams](https://nerd-notes.com/unit-2-3-drawing-fbds-right/)
4. [Unit 2.4 | Deriving Equations to Solve Linear Force Problems](https://nerd-notes.com/unit-2-4-solving-force-problems/)
5. [Unit 2.5 | Advanced Force Problems – Tension and Elevators](https://nerd-notes.com/unit-2-5-advanced-problem-solving-tension-and-elevators/)
6. [Unit 2.6 | Advanced Force Problems – Ramps (Inclines)](https://nerd-notes.com/unit-2-6-advanced-problem-incline-plane-problems/)
7. [Unit 2.7 | Advanced Force Problems – Pulley System [Current Lesson]](https://nerd-notes.com/unit-2-7-advanced-problem-solving-pulley-systems/)
8. Unit 2.8 | Advanced Force Problems – Multi-Body System

#### In this lesson you will learn: 

- Understanding simple pulley systems (called an Atwood Machine)
- Solving pulley problems (the long way)
- Solving pulley problems (the easy way)

### The basics

The most basic pulley system, also referred to as an Atwood’s machine, consists of 2 masses connected by a rope. The tension is the same throughout the entire rope. The rope goes around a massless pulley as shown below.

![](https://i.stack.imgur.com/3KUG7.jpg)

And what if the pulley had mass? Then the mass would create a force called “[Torque](https://nerd-notes.com/torque-in-10-minutes/)” which we will cover much later in Unit 6.

#### The direction of acceleration

The pulley system will always accelerate in the direction of the heavier mass.

### Solving Pulley Problems

There are two ways we can solve pulley problems.

1. Using our force frame worked covered in previous sections (the long way)
2. Solving as a system (the easy way)

I will explain how to do method one in the video below and cover method two in the next lesson (Lesson 2.8)

[Video for [course members only](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/)]

### PQ – Pulleys (Intermediate)

1. Two objects (49.0 and 24.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find the acceleration of the objects and the tension in the string.
2. A window washer pulls herself upward using the bucket–pulley system. She sits in the bucket, and when she pulls down on the rope the bucket moves up.
  - How hard must she pull downward to raise herself slowly at constant speed?
  - If she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucket is 72 kg.

### PQ – Pulleys (Advanced)

![](https://nerd-notes.com/wp-content/uploads/2023/10/pulley-of-table-diagram-1.png)
*Diagram 1 for Problem #1 and #2*

1. Block A (mA) of mass 13kg is held in place on a frictionless table. It is connected by a massless rope to Block B (mB) of mass 5kg, that is hanging off the table.
  - Find the acceleration of each block when the system is released from rest.
  - Now if Block A is released from rest 1.25m from the edge of the table. How long does it take to get there?
2. Let’s replicate the situation above. This time, however, the table has a coefficient of static friction of .4 (µs = .4) and a kinetic friction of .2 (µk = .4).
  - What minimum value of mA will keep the system from starting to move?
  - What value of ma will keep the system moving at constant speed?

![](https://nerd-notes.com/wp-content/uploads/2023/10/Screenshot-2023-10-04-at-16.11.58.png)
*Diagram 2. For problem #3.*

1. A block of mass m1 (5kg) is on a ramp (µk = .22) that is inclined at 20° above the horizontal. It is connected by a massless string to a block of mass m2 (8kg) that hangs over the top edge of the ramp.
  - What is the acceleration of the masses and the tension in the string?
  - If m1 = 8 kg, and the coefficient of static friction between m1 and the incline is 0.300, find the maximum value of m2 that will not make m1 slide up the incline.

### Lesson 2.7 Recap

In this lesson you learned how to solve pulley problems in two different way.

### Lesson 2.8 Preview

In the next lesson, we will take “solving problems as a system” to the next step. We will cover how to solve problems where there are 2 or more objects — similar to what we did with the pulley system.  ## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-2-7-advanced-problem-solving-pulley-systems/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-2-7-advanced-problem-solving-pulley-systems/