Calculating Forces on an Inclined Plane

1. If not already done, set up your EduBlocks account and create a Classroom for your class. Share the link to the Classroom with your students.
2. Create an Assignment in EduBlocks for the “Ramp Calculator,” with your desired due date.
3. Edit the Starter Project of the assignment to give the students something to build off of.
4. Include as much or as little starting point as you would like. For my Starter Project, I included the following code:|

Feel free to use the slides provided (1-12), physical demonstrations, and/or worked examples on the board for the following lesson.

1. Review net forces of objects on a flat plane. Using an example, remind students that normal force is always equivalent to the total force an object applies on a surface.
2. Rotate their thinking. Introduce the concept of rotated co-ordinates by showing how most of the forces they will use are dependent on the angle of the ramp and independent of the traditional directions of “up” and “down.”
3. Decompose the weight. Demonstrate how students can adapt the object’s weight to this new co-ordinate system by finding the x- parallel component and the y- perpendicular component of the force of gravity.
4. Use weight to find normal force. Show that, since normal force is equal to the force applied towards the surface, the magnitude of the normal force must be equal to the magnitude of the weight’s perpendicular component.
5. Find the object’s net force. Using the parallel component of the weight and the force of the ramp’s friction, show how to find whether an object is moving and that the net force is equal to this minuend of these two forces.
6. Find the maximum angle of static friction. Using the definition of normal force and static friction, show that every friction interaction has a specific angle at which it will no longer be able to hold an object, equal to the arctangent of the coefficient of static friction.
7. Worked example. There is an example question provided in the slides. Work the students through the logic to find the answer (0.39 kg, with a weight of 3.8 N).

The following steps correspond to slides 13-20 of the provided slides. They introduce basic concepts of programming in Python. They can be skipped if students are familiar already with Python.

1. The math library. Introduce students to the concept of a “library” of functions, then show the need for the math.py library in their code. Students should become familiar with the math.sin/math.cos functions, as well as the math.degrees and math.radians functions in order to convert degrees to radians and vice versa. Stress the importance of radians as the only angular unit that Python trigonometric functions will accept.
2. Variables. Define variables, drawing from students’ prior experience with mathematics and physics. Have students consider what variables will be necessary when calculating for net force on a ramp.
3. Input/Output. Show students the value of print functions, as well as taking input for variables. A few examples are provided. Additionally, introduce the concept of variable types, as they will need their values to be in the form of a float in order for the math to function properly.
4. Conditionals. One aspect of this assignment is understanding that if the force of static friction exceeds the parallel component of weight, the object will not move. This means that they will need to understand how to use a conditional if/else function to provide optionality in their program.

After acquainting students with these basics, introduce the assignment:

Provide the .pdf of these slides to students to use as a reference when completing the assignment.

Provide the students 1-2 in-class periods to work on this assignment. While they work, ensure that you are circulating the room to catch any student confusion or difficulty.

If a student is stuck starting, provide them with an example question and ask them to record their process for solving it, step by step. This can help them to find the logic they will need for the program. If they get stuck on the logic, they can work together with classmates to find the solution, or you can provide more assistance with probing questions (e.g. “how does the angle affect the motion of the object?” “what is the equation for static friction? how does that relate to weight?” “what is the relationship between the angles of the normal force and the angle of motion?”)

For difficulties finding the proper way to translate mathematical logic to the code, be more liberal with assistance. As their programming ability is a secondary concern to their understanding of the basic logic of the problem, feel free to help them as much as necessary.