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

Central Forces 2023 (3 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

Students' Task

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

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    The puddle
    differentials Static Fields 2023 (6 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?
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    Warm-Up

    Warm-Up (Welcome Activity Reviewing Material from Undergraduate Physics)

    This content is used in the Physics Department at OSU with incoming graduate students to remind them of undergraduate content before classes start and to help them to decide whether or not to take some Bridge Courses. This sequence is intended to run in two blocks of three hours each. The sessions should be run by someone with a deep knowledge of all of the relevant courses, the specific activities, and active engagement in general.

    This session may be the first opportunity for the incoming graduate students to meet each other as well as some faculty and other graduate students. So start with a 1/2 hour dedicated to introductons.

    Consider inviting some or all of the following people to participate:

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    • Graduate students who have TAd for courses that incorporated these exact activities, as needed to provide one experienced person to sit with each group of three graduate students. The Head Graduate Advisor has often asked these graduate students for evaluative input regarding the members of their group. CAM thinks that they should be given a heads-up about what will be expected.
    • The Head Graduate Advisor (n.b. In the past the Grad Advisor has roamed the classroom, hovering over the groups as they work. CAM thinks this can appear intimidating/judgmental. Consider asking the grad advisor to SIT with groups, even if they move frequently from group to group.
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    • Faculty who will be teaching the Bridge Courses so that they are available to answer student questions, especially individual questions during breaks.
    • Graduate students who have take Bridge Courses in the past who are comfortable discussing their choices and experiences.

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Learning Outcomes