1. Reviewing center of mass, conservation of momentum, and conservation of angular momentum.

Estimated Time: 15 minutes

A group of students tethered together are floating freely in outerspace. Their task is to devise a method to reach a food cache some distance outside their group.

Some knowledge of center of mass. Introductory physics is sufficient.

• Several pieces of string (enough to connect each pair of team members), each approximately 5 ft in length.

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:

1. Newton's Laws hold.
2. Each person must stay tethered to the group by at least one string.
3. 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.)

The goal of this activity is to get the students discussing the concept of center of mass.

Many (surprisingly many!!!) students will propose scenarios that violate conservation of either linear or angular momentum. 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. This is a good example of how many students at this level are not used to using reasoning based on the laws of physics.

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.

An interesting solution that is often 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.

This activity naturally leads into a formal derivation and discussion of center of mass and the conservation laws. It is important for students to realize that by arranging themselves along a straight line, they are the longest they can be. It is also important for them to reach the conclusion that 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.