## Activity: Survivor Outer Space: A kinesthetic approach to (re)viewing center-of-mass

Central Forces 2022 (2 years)
A group of students, tethered together, are floating freely in outer space. Their task is to devise a method to reach a food cache some distance from their group.
• group Small Group Activity schedule 10 min. build Several pieces of string (enough to connect each pair of team members), each approximately 5 ft in length.
What students learn
• Review center-of-mass for a system of particles;
• Review the consequences of conservation of momentum--without external forces, the center-of-mass of a system of mass can't change velocity;
• Review the consequences of conservation of angular momentum--without external torque, the total angular momentum of a system of particles can't change. -Reviewing center of mass, conservation of momentum, and conservation of angular momentum.

## Instructors Guide

A group of students, tethered together by strings, imagine themselves to be floating freely in outerspace. Their task is to devise a method to reach a food cache some distance from their group.

## Props/Equipment

• Several pieces of string (enough to connect each pair of team members), each approximately 5 ft in length.
• You can suggest in your course schedule or syllabus that students bring a space suit to class. Those students who respond to the prompt "Who brought a space suit to class," can be rewarded for their dilligence by being chosen to play the game. This gives you a good idea of who is reading the course materials.

## Introduction

A group of five students are chosen to participate in a game of Survivor, set in beautiful, sunny outerspace. These students are brought to the front of the class and thethered together in a group. In order to survive, they must reach a food cache placed about 20 ft from their group. The whole class is given the task of devising a method by which the students can reach the food cache without losing any members of the group.

Rules:

• Newton's Laws hold.
• Each person must stay tethered to the group by at least one string.
• You have no free masses to throw or other propulsion devices. (You can tell them this rule AFTER they propose a solution that involves ejecting a person or an air canister. They need to learn that, in the work world, their boss may not appreciate impractical or immoral solutions to problems.)

## Student Conversations

The goal of this activity is to get the students discussing the concept of center-of-mass and the consequences of the laws of conservation and angular momentum.

Many (surprisingly many!!!) students will propose scenarios that violate conservation of either linear or angular momentum. This is a good example of how many students at this level are not used to using reasoning based on the laws of physics. While a few students may call out these conservation laws, if the instructor ignores them, they will vary rarely follow through with an explanation of why these laws are relevant.

Students often get distracted by the details of the procedure they will carry out, e.g., how will they initiate propulsion to spread out the group. It is important to ultimately refocus the discussion onto the constraints on their motion implied by the conservation laws.

Eventually, they should reach the conclusion that they cannot change the center-of-mass of the group. By stringing themselves out in one-dimension makes the longest shape. By putting the heaviest group members on the side opposite the food allows the lightest members on the side near to food cache to extend out the maximum amount.

An interesting solution that is occasionally brought up by students is to wait for the gravitational attraction between them and the food to bring the food to them. Calculating the time it will take for the food to reach them by gravitational attraction alone might make an interesting homework problem.

## Wrap-up

This activity naturally leads into a formal derivation and discussion of center-of-mass and the conservation laws.

Watch the classroom dynamics as you do this activity. Depending on how the classroom dynamics work out, this activity can form a good basis for a class discussion about equity: examining whose ideas were taken up by the class, who felt comfortable calling out answers, etc. At a minimum, make sure to publicly acknowledge the students that had quietly expressed good ideas that were ignored by the class or by you. Also make sure to avoid any fat shaming of the heaviest member of the group.

• assignment The puddle

assignment Homework

##### The puddle
differentials Static Fields 2022 (4 years) The depth of a puddle in millimeters is given by $h=\frac{1}{10} \bigl(1+\sin(\pi xy)\bigr)$ Your path through the puddle is given by $x=3t \qquad y=4t$ and your current position is $x=3$, $y=4$, with $x$ and $y$ also in millimeters, and $t$ in seconds.
1. At your current position, how fast is the depth of water through which you are walking changing per unit time?
2. At your current position, how fast is the depth of water through which you are walking changing per unit distance?
3. FOOD FOR THOUGHT (optional)
There is a walkway over the puddle at $x=10$. At your current position, how fast is the depth of water through which you are walking changing per unit distance towards the walkway.
• group Heat and Temperature of Water Vapor (Remote)

group Small Group Activity

5 min.

##### Heat and Temperature of Water Vapor (Remote)

In this introduction to heat capacity, students determine a derivative that indicates how much the internal energy changes as the temperature changes when volume is held constant.
• assignment Symmetry Arguments for Gauss's Law

assignment Homework

##### Symmetry Arguments for Gauss's Law
Static Fields 2022 (4 years)

Instructions for 2022: You will need to complete this assignment in a 15 minute appointment on Zoom or in person with one of the members of the teaching team between 1/21 and 10 pm on 1/26. Here is a link to a sign-up page.

You are required to watch a sample video for how to make symmetry arguments here. As demonstrated in the video you should bring with you to the meeting a cylinder, an observer, and a vector.

Use good symmetry arguments to find the possible direction for the electric field due to a charged wire. Also, use good symmetry arguments to find the possible functional dependence of the electric field due to a charged wire. Rather than writing this up to turn in, you should find a member of the teaching team and make the arguments to them verbally.

• group Establish Classroom Norms

group Small Group Activity

60 min.

##### Establish Classroom Norms
Theoretical Mechanics 2021 (2 years)

In this hour-long activity, students establish classroom norms for being respectful when working in small groups. This is particularly helpful in the first course a cohort of students encounters.
• group Mass is not Conserved

group Small Group Activity

30 min.

##### Mass is not Conserved
Theoretical Mechanics 2021 (2 years)

Groups are asked to analyze the following standard problem:

Two identical lumps of clay of (rest) mass m collide head on, with each moving at 3/5 the speed of light. What is the mass of the resulting lump of clay?

• group Number of Paths

group Small Group Activity

30 min.

##### Number of Paths

Student discuss how many paths can be found on a map of the vector fields $\vec{F}$ for which the integral $\int \vec{F}\cdot d\vec{r}$ is positive, negative, or zero. $\vec{F}$ is conservative. They do a similar activity for the vector field $\vec{G}$ which is not conservative.
• group Thermodynamic States (Remote)

group Small Group Activity

30 min.

##### Thermodynamic States (Remote)

Try doing this activity as a follow-up to the Changes in Internal Energy (Remote) about the first law of thermodynamics.
• face Central Forces Introduction: Lecture Notes

face Lecture

5 min.

##### Central Forces Introduction: Lecture Notes
Central Forces 2022
• computer Using Technology to Visualize Potentials

computer Mathematica Activity

30 min.

##### Using Technology to Visualize Potentials
Static Fields 2022 (4 years)

Begin by prompting the students to brainstorm different ways to represent a three dimensional scalar field on a 2-D surface (like their paper or a whiteboard). The students use a pre-made Sage code or a Mathematica worksheet to visualize the electrostatic potential of several distributions of charges. The computer algebra systems demonstrates several different ways of plotting the potential.
• group Vector Integrals (Contour Map)

group Small Group Activity

30 min.

##### Vector Integrals (Contour Map)

Learning Outcomes