It is possible for objects to share similar motions with other objects, an example would be a car and the driver, both are traveling at the same speed and direction. When scenarios like this occur, we call it a coupled system. This section will help develop the necessary tools to identify coupled systems and the resulting constraints that arise from this coupling.
In coupled system we often have to think about which objects have the same motion or some known relative motion. Those objects that do move together can be grouped into one system with multiple objects inside and the acceleration of the whole will equal that of the individual pieces. They may also be constrained together in some way. Think of all the objects that move together, the constraints on their motions, and the Newton's 3rd law force pairs in the video below.
https://www.youtube.com/watch?v=t6dWQck6jkA
Mechanical advantage is measure of how much effort it to do something without a device, such as lifting a mass, divided by how much it takes to do that with the aid of a device, such as lifting the mass with a pulley system. Mechanical advantage tells us how much easier a job is with a tool than without. A ramp with a wheelbarrow, a bikes gears, a pulley system, theses are all examples of simple machines used to create mechanical advantage.
This video will help orient us towards what a pulley system is. We'll have to go deeper into the analysis but is a good start.
https://www.youtube.com/watch?v=LiBcur1aqcg
Pre-lecture Study Resources
Read the BoxSand Introduction and watch the pre-lecture videos before doing the pre-lecture homework or attending class. If you have time, or would like more preparation, please read the OpenStax textbook and/or try the fundamental examples provided below.
BoxSand Introduction
Forces | Coupled Systems and Pulleys
Many mechanics problems involve two or more objects being connected together. An example could be two masses connected by a pulley, or one block stuck to another block, possible through friction. We call these coupled systems. These systems are often connected by third law force pairs, or just force pairs. And when any two objects are coupled together they must share something in common, such as the magnitude of a tension force or the magnitude of their kinematics variables.
BoxSand Videos
OpenStax Reading
OpenStax Section 4.4 | Newton's 3rd Law of Motion: Symmetry of Forces
Fundamental examples
Worked Examples
Box pulled on top of another box
Box pushing on suspended second box
1. Consider the image below. The $7 \, kg$ mass rests on top of a frictionless table, and is connected to a massless string hung over a massless frictionless pulley. Find the magnitude of acceleration for both masses.
2. Consider the image below. The $7 \, kg$ mass rests on top of a frictionless table, and is connected to a massless string hung over a massless frictionless pulley. Find the magnitude of acceleration for both masses.
Short foundation building questions, often used as clicker questions, can be found in the clicker questions repository for this subject.
Post-Lecture Study Resources
Use the supplemental resources below to support your post-lecture study.
Practice Problems
Recommended example practice problems
BoxSand's Quantitative Practice Problems
BoxSand's Multiple Select Problems
Solutions to BoxSand Practice Problems
Universal Gravity Practice Problems
Solutions to Universal Gravity Practice Problems
Set 1: Problem 1 Problem 2 Problem 3
Set 2: Stacked Boxes
Set 3: Ropes and Pulleys
For additional practice problems and worked examples, visit the link below. If you've found example problems that you've used please help us out and submit them to the student contributed content section.
Additional Boxsand Study Resources
Additional BoxSand Study Resources
Learning Objectives
Summary
The goal of studying coupled systems is to apply Newton's laws of motion, with an emphasis on the 3rd law to situations with multiple objects. In these cases decisions about how to define the system(s) will be confronted.
Atomistic Goals
Students will be able to...
- Analyze situations involving multiple objects and choose appropriate systems.
- Differentiate between external and internal forces.
- Use 3rd law force pairs to analyze coupled systems.
- Use constraints to analyze coupled systems.
- Choose coordinate systems relative to each other that simplify the analysis.
- Choose different systems (e.g. the system 1 and 2, or the combined 1 2 system) for the same physical situation and use the analysis from both to arrive at a solution.
- Identify the features of an ideal pulley.
- Demonstrate the ability to use a FBD and Newton's 2nd law to determine the mechanical advantage of a pulley system.
 |
 |
 |
 |
 |
Additional Study Resources
Use the supplemental resources below to support your post-lecture study.
YouTube Videos
Simulations
PhET Springs: A fun little applet that looks at springs. Don't worry about any of this normal mode stuff, just explore how changing one spring might effect another.
Atwoods Machine: Another Wiley interactive simulation directly applying concepts from Newton's 2nd Law;
For additional simulations on this subject, visit the simulations repository.
Demos
For additional demos involving this subject, visit the demo repository
History
Oh no, we haven't been able to write up a history overview for this topic. If you'd like to contribute, contact the director of BoxSand, KC Walsh (walshke@oregonstate.edu).
Physics Fun
Oh no, we haven't been able to post any fun stuff for this topic yet. If you have any fun physics videos or webpages for this topic, send them to the director of BoxSand, KC Walsh (walshke@oregonstate.edu).
Other Resources
Physics Classroom: Good introduction with examples, and it has a great lay out that will lead you through different coupled systems and works example problems to show you how objects might interact.
If you'd like to find out more about constraints this web page has some great examples. Specifically look at example 2 and 3;
Resource Repository
This link will take you to the repository of other content on this topic.
Problem Solving Guide
Use the Tips and Tricks below to support your post-lecture study.
Assumptions
Checklist
Misconceptions & Mistakes
Pro Tips
Multiple Representations
Multiple Representations is the concept that a physical phenomena can be expressed in different ways.
Physical
Mathematical
Graphical
Descriptive
Experimental