# Introduction to Forces on an Inclined Plane

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## Objective

Students will uncover the ways that an object's weight is distributed into orthogonal components on an inclined plane.

#### Big Idea

On a ramp, one feels the gravitational force, but not all of it is directed downhill. We can look at data to decode how the weight of an object is distributed on a ramp.

## Overview

I am faced today with two constraints: I am out of class for the next lesson, the plan for which includes a virtual exploration at a web-based simulation, and today's lesson is shortened due to an assembly schedule. To enable student success in the next class, I need to provide a bit of a background this class.

The goal for today and the next class is to expand student thinking about Newton's Second Law of Motion (NGSS Performance Expectation HS-PS2-1). They are familiar with the process of drawing free-body diagrams that lead to net force equations. The complicating aspect of an inclined plane, introduced here, challenges student thinking about the conventional separation of forces into horizontal and vertical components. The weight of an object does get resolved into orthogonal components, with the angle of the plane determining the rotation of those forces. Students collect data, use their Newtonian Analysis skills, and attempt to induce the relationships between an object's weight and its normal and parallel forces. In so doing they develop and use models (Science & Engineering Practice #2), they plan and carry out an investigation (#3), they analyze and interpret data (#4) and they use mathematics and computational thinking (#5).

## Warmup and Video Demonstration

20 minutes

As a follow-up to our previous lesson, I provide a warmup today that is based on the exchange of potential and kinetic energies in a frictionless environment. The interesting angle of this problem is that the original height is never defined, though the initial potential energy is given.

Students work individually or in small groups as I move around the room to provide hints, suggestions, and feedback. Many students are eager to solve for the original height, which is possible though not strictly necessary. Indeed, some insightful students note that each height in the problem is stated as a portion of the original height - potential energies can be calculated as a portion of the potential energy at the start. I don't prevent students from finding the original height, but I do alert them that it is possible to solve the problem without the benefit of that knowledge.

Students work on this problem in their notebooks for about six or seven minutes when I given them a two-minute warning to finish up. I then show a solution at the board, highlighting the proportional thinking mentioned above.

As a visual treat, I take a few minutes to show Walter Lewin, an MIT Physics professor, demonstrating the conservation of energy and banking on the fact that a released bowling ball will not gain height as it travels at the end of a pendulum. Here's the link to that lecture. The clip starts at the right place and is about nine minutes long.

## Identifying Gravitational Forces on a Ramp

30 minutes

During this segment of class, I want to expand student thinking about the normal force and introduce a companion force known as the "parallel force." These are both related to the weight of an object and have important roles to play in any analysis that involves inclined planes or ramps. Students need these ideas as they pursue more sophisticated versions of Newton's Second Law.

I hand out a template that has two identical drawings on it while I simultaneously display the diagrams on the board. The left-hand diagram is used in response to the prompt below it while the right-hand image is used, if necessary, for students to draw in a clean version of our final thoughts. I want students to make conjectures about the directions of the weight, the normal force, and the frictional force, then amend their drawings, if necessary, after a short discussion about these forces.

Through a conversation, students and I agree that on the directions of the named forces and also agree that there must be another force (identified by the ?) that motivates the block down the ramp. This force obviously needs a name and, given its direction with respect to the plane, we call it the "parallel force" or Fp.

I then ask my students to respond to a simple task; to look at four different ramps and try to draw in the weight, the normal, and the parallel forces in the right directions and with an approximate sense of scale. In other words, make Fn the largest at the angle one thinks it is largest, and smallest where one thinks it to be smallest. Here are their results, collected at the board, after a brief conversation.

As a final task, to summarize our thinking about these forces, I ask students to make sketches in their notebooks of what shape they think these forces have as the ramp angle is altered from 0 to 90 degrees. I give them just two minutes to think and discuss with one another, then have students come to the board to draw in their conjectures. The results are encouraging: the gravitational force is unaffected by angle and the normal and parallel forces each change in the correct directions, though with multiple possible shapes identified. The exact shape is the goal of next week's investigation and it is a hopeful sign that the students can see the general trend of these forces.

Given this background, I move quickly to show the simulation that allows manipulation of an inclined plane. There are a couple of pitfalls to avoid and I want students to see them before beginning.

## Preview of Ramp Simulation

10 minutes

I quickly use my Smartboard to navigate to the University of Colorado's PhET website and access The Ramp simulator. I also hand out some notes that help students negotiate some of the issues that are prevalent with this simulation. The notes contain a link to a video I created to review some of the hints and tips that I share here in the final few minutes of class.

The most important idea that students need to understand is that each trial MUST start with the object at the top of the ramp and with zero initial velocity. The entire calculation of acceleration, and therefore the net force, depends upon this assumption. This may seem a bit arbitrary to students as I have not yet handed out the instructions for the investigation, but I am hopeful that seeing it once with me, then reviewing it as a video later, will have the desired impact.

My vision is to have students collect data, use their Newtonian Analysis skills, and attempt to induce the relationships between an object's weight and its normal and parallel forces. In so doing they develop and use models (Science & Engineering Practice #2), they plan and carry out an investigation (#3), they analyze and interpret data (#4) and they use mathematics and computational thinking (#5).

I take the final few minutes to demonstrate the use of the simulation, to review the hints on the handout, and to address any questions from students.