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TERMINAL VELOCITY WITH PORTAL 2

Students build a simple experiment to compare the terminal velocity of a cube and Chell, also investigating the math behind air resistance and terminal velocity.

grade level:
9-12
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Created by
Cameron Pittman

PORTAL 2 - EDUCATION VERSION overview

The Portal 2 - Education Version is a custom modification of Portal 2, the critically acclaimed single-player puzzle game from the developers at Valve. This modified version of Portal 2, along with a game called Universe Sandbox, is part of a program Valve is calling Steam for Schools (not to be confused with the STEAM education movement that shares the same name), in which they hope to encourage teachers to use their games to teach standards-based curriculum.
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Experience breakdown

Lesson Plan Overview

Time Needed: 60 Minutes

Vocabulary: Terminal Velocity, Friction, Air Resistance, Forces, Free Fall

Student Prerequisites: velocity, friction, forces

Teacher Materials Needed: None

Student Materials Needed: Stopwatch

Standards: For a full list of standards covered in this lesson plan, please refer to this page.

The video below offers an overview of the various objects, features, and mechanics in Portal 2 that will be used in this lesson plan, as well as how the game can be used to teach terminal velocity.

Terminal Velocity

This lesson plan was developed with the idea that the educator understands physics and the basics of Portal 2. The lesson itself should flow from an introduction, into a main lab activity, and then finish with follow up questions and a homework assignment.

  1. The Introductory Activity section starts with questions to ask students at the beginning of class or in the class prior.
  2. The Implementation section gives instructions to the instructor as to how to set up the main lab activity.
  3. The Closing Activity section lists questions for students after they complete the main lab activity.
  4. The Homework section suggests questions to assign as homework after the lab.
  5. The Grading Advice section gives answers to all of the questions in the Introductory Activity, Implementation, Closing Activity, and Homework sections.
  • I’m always looking for better lessons or ideas. If you have any questions or comments, please contact me at: cameron *dot* w *dot* pittman *at* gmail *dot* com.
  • This lesson plan is meant to be a set of guidelines, not instructions. It is meant to be disassembled, reconfigured and reconstructed to fit your students and your teaching style.

Learning Objectives

  • Demonstrate the effects of air resistance on terminal velocity.

Lesson Steps

I. Introductory Activity

1. Diagram the forces present on a falling skydiver.

Screen_shot_2013-08-19_at_11.13.42_am

2. Terminal velocity is the fastest an object will move solely under the influence of gravity. At terminal velocity, how will the vertical forces on a skydiver compare? Why?

3. What can a skydiver do to change their terminal velocity?

4. Compare and contrast the terminal velocity of a falling sheet of paper (non-crumpled) and a falling wad of paper (crumpled). How does the shape of the paper affect the way it falls?

5. An alien from Venus is visiting Earth. On Venus, the atmosphere is much thicker. Let’s assume the strength of gravity on the Earth is about the same as it is on Venus (Venus’ gravity is actually just a bit less). If the Venusian alien jumps out of a space ship and falls towards the Earth, how will their terminal velocity in Earth’s atmosphere compare to their terminal velocity on Venus? Why?

II. Implementation

1. (Recommended) Discuss the introductory activity questions first. Have students act out question 4 if necessary or if time allows.

2. Students will build a very simple infinite fall (two portals on top of one another).

3. Students should make the ceiling four panels high, so as to make it easier to count the number of falls. See example below.

Screen_shot_2013-08-19_at_11.33.40_am

NOTE: An easy way to create an infinite fall (pictured above) is to shoot a portal directly below you as you are falling from the ceiling.

4. Students will use a stopwatch to record the time it takes for a cube to make five full drops through the room at terminal velocity (hint: listen to the ‘woosh’ sound made by moving through a portal to figure out the number of falls). Students should wait a few seconds until it becomes clear the cube has reached terminal velocity. Fill out table 1, which can be accessed here.

5. Repeat step 4 four more times.

Screen_shot_2013-08-19_at_11.52.47_am

Dropping a cube in the infinite fall.

6. Repeat steps 4-5 using Chell as the falling object.

Screen_shot_2013-08-19_at_11.52.04_am

Chell (i.e. the player) going through the infinite fall.

III. Closing Activity

1. Complete the calculations at the bottom of table 1.

2. How do the terminal velocities of Chell and the cube compare? Which is faster? Why?

3. Predict the terminal velocity of a flatter, lighter companion cube.

4. If you noticed a discrepancy between the terminal velocities, what reason might the game developers have for programming a difference?

5. Terminal velocity can be found by: vterminal = mgb (1), where b represents the strength of air resistance.

a. What are the units of b?

b. If the mass of an object increases, how does terminal velocity change?

c. If air resistance is stronger, how does terminal velocity change?

6. What was the purpose of repeating our measurements five times?

IV. Homework

Oh no! GLaDOS is trying to kill Chell again with deadly neurotoxin. In order to escape, Chell jumps down what looks like an infinitely deep pit and reaches terminal velocity on the way down. Let’s assume that Chell has a mass of 50 kg and gravity within Aperture Labs is 9.8 m/s2.

a. If the deadly neurotoxin flooding the air increases b from 3.2 N-s/m to 4.5 N-s/m, by how much will Chell’s terminal velocity decrease?

b. How else could Chell slow herself down before reaching the bottom of the pit?

Grading aDvice

I. Introductory Activity:

1. Falling skydiver:

Screen_shot_2013-08-19_at_12.10.04_pm

Fd = force of drag, Fg = force of gravity

2. The force of gravity and drag force equal each other at terminal velocity.

3. A skydiver can angle their body to minimize friction.

4. A wadded piece of paper feels less drag because it presents a smaller surface area to the air. A flat piece of paper presents a large surface area and feels much more resistance.

III. Closing Activity:

3. A flatter, lighter cube has more friction and would have a lower terminal velocity.

4. Different objects need to behave differently in a game in order for certain puzzles to work.

5. a. Rearrange equation 1 to find that: b = mgvterminal (2). The unit for m is kg, v is m/s, and g is m/s2, so the final unit for b will be: kg/s

b. Terminal velocity increases.

c. Terminal velocity drops.

IV.Homework:

a.Starting with equation 1. Set b1 = 3.2 N-s/m and b2=4.5 N-s/m.

vterminal = mgb (3)

Δvterminal = mgb2 - mgb1 (4)

Plug in and we get Δvterminal = -44m/s

b. She could increase her surface area by falling in a spread eagle position.

Additional Activities

  • If your students have already calculated g, you can determine m/b .
  • Calculate error on student measurements.
  • Replicate experiment using turrets or other kinds of cubes.
  • If possible, change the force of friction and repeat experiment.
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