Teacher Notes for Forces in Two Dimensions
Unit Overview
Our
Vectors and Projectiles unit was relatively heavy on the math and lighter on the concepts. This Forces in Two Dimension unit is even more so. The unit includes four basic types of problems:
- Equilibrium Problems (most often, a sign hanging problem)
- a=Fnet/m Problems with a Force at an angle to the acceleration
- Inclined Plane Problems
- Two Body Problems with Pulleys
The first three problem types require the use of a trigonometric function to resolve all forces so that they are along the x-y axes. The fourth problem type requires two free-body analyses in order to generate a system of two equations to solve for the two unknowns. The inclined plane problem type includes the added complication of re-defining the x-y axes such that they are parallel and perpendicular to the inclined plane. Some of the two-body problems may also include an inclined plane and require axes re-definitions. We have suggested nine days for completion of the activities for these four problem types.
The Calculator Pad (a.k.a., CalcPad)
When it comes to solving Physics word problems or simply conducting a mathematical analysis of a physical situation, our CalcPad section is the go-to resource. We have nearly 75 ready-to-use problems organized into 14 different short problem sets for the topic of
Forces in Two Dimensions. With a Task Tracker subscription, you can organize the pre-made problems into your own problem sets and even write your own problems. We have created five different custom problems sets for this unit that represent a re-organization of those ~75 problems. With a Task Tracker subscription, you can assign these to your students and even edit them by removing or adding problems.
Physics Interactives
We have suggested two different Physics Interactives in our Lesson Plans. Both pertain to equilibrium problems. They are
Go For the Gold and
Balance It! Both are skill-building exercises divided into different difficulty levels. Preview them ahead of time and assign those levels that are most suitable to your students. If you have a Task Tracker subscription, you can assign the Interactives and then tap the Trash can next to a level to remove it from your student's experience. We will put a great big red X through that level when your students arrive at the main menu. Use the Preview page (Teacher Resources section of your account) to quickly preview each level of the Interactive.
And More Physics Interactives
We have two additional simulations that will have great value for the two-body problems. Our
Atwoods Machine simulation from the Newton's Laws chapter provides an environment that allows the learner to explore two-mass systems. An Atwood's machine (two masses connected by a string that stretches over a pulley) and a modified version of the Atwood's machine (one of the masses is on a horizontal surface) can be explored. The environment allows a user to change the amount of mass, introduce friction into the horizontal surface and measure the time for the system to move a particular distance.
Our
Atwoods Machine 2D simulation from the Forces in 2 Dimensions chapter provides nine scenarios to investigate. There are multiple variables that can be altered depending on the scenario. A Graphical menu allows users to quickly navigate between scenarios. Variables include the masses of the two objects, the angle of the surfaces along which they move, the coefficient of friction with the surfaces, the initial velocity of the system, and the rotational inertia of the pulley.
Depending on the depth to which you wish to cover two-body problems, the addition of an extra day and the use of the simulations may be a worthwhile adjustment.
It's "Honors" Physics
Often times our Lesson Plans and the Learning Outcomes for our
on-level Physics course and our Honors Physics course do not look a whole lot different. But when you begin to look below the surface you are going to notice less-than-subtle differences. For this unit, there is the additional topic of two-body problems. We have added a Tutorial page, a tutorial video, a Think Sheet, a lab, and an additional problem set for coverage of the topic.
In addition to that change, we have also utilized different problems in our CalcPad problem sets. The problems are more difficulty for the Honors Physics sets and often times include the use of kinematic equations. We have also suggested different difficulty levels for some of the Concept Builders and Interactives. It is not unusual to get some push-back from students when challenges arise. In many cases (maybe all cases ... but the teacher should be the judge), the challenge level is appropriate and should serve as a reminder to complaining students that they have enrolled in an HONORS Physics.
Other Resources
There are a few resources that we did not list in our
Lesson Plans and
Learning Outcomes and Activities that you may find to be very helpful or more
in-style with your approach. These include:
- Concept Builder: Equilibrium
Students use concepts of equilibrium and vector components in order to add two forces to an object so as to establish an equilibrium state.
- Minds On Physics: Mission F2D2 on Fnet = m•a and Forces at Angles
Students conduct an analysis of situations involving angled forces on objects that accelerate across a horizontal surface. Friction and no-friction cases are considered. Includes several structured problems.
- Minds On Physics: Mission F2D4 on Static Equilibrium Analysis
Students analyze situations in which a sign is hung by two or more angled cables. Includesn both forced choice questions and multi-blank numerical analyses.
- Minds On Physics: Mission F2D6 on Inclined Plane Analysis
Students conduct an analysis of an object on an inclined plane. Includes several structured problems.
- Physics Interactives, Newton's Laws: Atwoods Machine
Students explore the physics of an Atwoods machine (two masses attached by a string wrapped around a pulley) and a modified Atwoods machine (one mass is on a horizontal surface with the second mass suspended over the pulley).
- Physics Interactives, Forces in Two Dimensions: Atwoods Machine 2D
Students explore a multitude of situations involving two objects, a pulley, and a string connecting them. The simulation allows one to compare situations quite quickly to draw parallels between them.
Law of Conservation of Time
As we mentioned in our Vectors and Projectiles unit, classes that have great difficulty with the mathematical aspect of Physics may wish to take a pass on this unit. The time might be better spent on some new ideas (momentum conservation, energy conservation, circular motion, etc.). As we say, the total amount of time in a school year cannot be created nor destroyed; but it can be transferred from one unit to another. Make the decision which works best for your classroom and students.
Teacher Presentation Pack
Yes. This is going to cost you ... money. But it is also going to pay you back big time in return ... time and the satisfaction that comes with managing your class and providing engaging lessons. Our
Teacher Presentation Pack was designed for all Physics teachers; but we particularly had early-career and cross-over Physics teachers in mind. For them (and anyone), this can be a huge time saver and a life saver (excuse the slight exaggeration). It includes a large collection of Slide Decks, Lesson Notes, animations, and graphics for use in your classroom. Once downloaded, you can modify and customize the Slide Decks as needed. The slides are highly organized and (mostly) graphical; they make great graphic organizers for any student, and especially for the struggling student. Learn
more.
Also Available ...
Physics teachers may find the following
for-sale tools to be useful supplements to our Lesson Plan and Pacing Guide section:
- Task Tracker Subscription (annual purchase)
A subscription allows teachers to set up classes, add students, customize online assignments, view student progress/scores, and export student scores. Task Tracker accounts allow your students to begin assignments in class or at school and to finish them at home. View our Seat and Cost Calculator for pricing details.
- The Solutions Guide
We publish a free curriculum with >200 ready-to-use Think Sheets for developing physics concepts. The Solutions Guide is a download containing the source documents, PDFs of source documents, and answers/solutions in MS Word and PDF format. An expanded license agreement is included with the purchase. (Cost: $25 download)
- Teacher Presentation Pack
This is a large collection of downloadable content packed with nearly 190 Microsoft PowerPoint slide decks, the corresponding Lesson Notes (as PDF and fully-modifiable MS Word format), about 170 animations (in .gif, .png, and .mp4 file formats), a countless number of ready-to-use images (including the original source documents that would allow for easy modification of those images), and a license that allows teachers to modify and use all the content with their classes on password-protected sites (such as course management systems). (Cost: $40 download)
- Question Bank
We distribute a Question Bank that includes more than 9300 questions neatly organized according to topic. The Question Bank is the perfect tool for busy teachers or new teachers. Even if you don't use the website with your classes, the Question Bank will assist you in quickly putting together quizzes, tests and other documents with high-quality questions that target student's conceptions of physics principles. And if you do use The Physics Classroom website, the Question Bank is the perfect complement to the materials found at the website. (Cost: $25 download)