## Main Sequence Stars: A System in Equilibrium?

### Robert Rosen

#### Description

Studentsunderstand and describe the equilibrium of internal forces in a main sequence star.

#### Objectives

The student understands stellar equilibrium.

The student knows that investigations are conducted to explore new phenomena, to check on previous results, to test how well a theory predicts, and to compare different theories.

#### Materials

-Moment of force (torque) balance
-Large weight
-Small weight
-Plastic soda bottle

#### Preparations

A discussion of equilibrium may be necessary prior to this activity. The following lesson may help prepare students.
1. The instructor uses examples to introduce the concept of equilibrium.
Set up the moment of force balance so that a large weight is suspended close to the center of a meter stick and a small weight is hung on the opposite side of the center. Adjust the location of each mass until the meter stick is in rotational equilibrium; that is, until the stick is balanced as shown in the illustration found in the attached file.

Next, cut a hole near the bottom of a plastic soda bottle. Allow water to pour into the bottle from the top. Adjust the rate at which water is added to the bottle so that the level of water in the bottle remains constant.

Ask students what the two systems have in common.

Answer: Both systems are in equilibrium. There are opposing forces or processes in each system. The forces or processes balance each other so that the state of the system does not change. Consider the torque balance. The large weight would turn the meter stick counterclockwise if it acted alone. The small weight would cause a clockwise rotation if it acted alone. The tendency of the bar to turn counterclockwise is balanced by the tendency of the bar to turn clockwise, so the bar remains motionless. Consider the plastic bottle. The water level in the bottle is constant because the rate at which water leaves through the hole at the bottom equals the rate at which water pours in at the top.

2. The instructor describes a system in equilibrium that we often see in the real world.
Consider the express lane at a grocery store. Suppose that customers arrive at a steady rate and each buys about the same number of items. The length of the line remains constant if the rate at which people enter the line equals the rate at which customers get checked out.

The instructor may wish to explain the difference between static and dynamic equilibrium. The grocery store line is in dynamic equilibrium. There is a balance between two active processes—customers leaving the line and new people entering the line. The number of people in line is constant, but the individuals making up the line are constantly changing. An advertising display that uses a row of pictures of athletes could be thought of as a line in static equilibrium. The number of items in the line is constant because nothing leaves the line and nothing enters it. The items making up the line do not change.

Background:
The following examples of systems in equilibrium are provided as a resource for the instructor. The opposing forces or processes are identified for each system.
*The population is constant in a certain country. (The number of births equals the number of deaths.)
*The price of salt is constant. (The supply of salt equals the demand for salt.)
*Water level in an open bottle drops each day because water evaporates from the bottle. The water level in a sealed bottle does not change. (In a sealed bottle, the rate of evaporation is balanced by the rate of condensation.)
*Despite evaporation under a hot sun, Florida does not become a desert. (The evaporation rate equals the precipitation rate.)
*A parachutist falls at a constant rate. (Upward drag exerted by the air on the parachute balances the downward force of gravity.)
*Neither side wins a tug-of-war. (The force exerted by one team is equal in magnitude to the force exerted by the other.)
*A person's body temperature remains constant at 98.6F. (Heat is generated inside the body at the same rate it flows to the environment.)
*A checking account balance remains constant. (Deposits into the account are made at the same rate as money is withdrawn.)
*The number of cartons of ice cream in a grocer's freezer is constant. (New stock is added to the freezer at the same rate that ice cream is bought.)
*In the Millikan oil drop experiment, charged oil droplets remained stationary in an electric field. (The upward electrical force on a droplet balanced the weight of the droplet.)

#### Procedures

Knowledge/Skills:
-Students will understand the concept of equilibrium.
-Students will relate equilibrium of forces to stellar equilibrium.
-Students will utilize reading and writing skills to enhance concept development.

Procedure:
1. Explain the assignment.
Tell students to analyze a system that is in equilibrium. The system can be one they learned about in school or it can be a system they encountered in everyday life. Students must first describe the system. The students must then identify the opposing forces or processes that work to produce the equilibrium. Remind students that their work will be assessed based on the accuracy of the information they provide, the clarity of their writing, and the mechanics (grammar, spelling, sentence structure, and variety of sentence structure) of their writing.

2. Student volunteers present their descriptions.
Student presentations should provide the class with varied examples of systems in equilibrium. After each student volunteer presents a description of the system, the class should identify the opposing forces or processes that operate in the system.

3. Students research stellar equilibrium.
A star is an example of a system in equilibrium. Most earth science textbooks describe the structure of the sun and the processes that occur inside the sun. Assign reading about this material. Have students write a brief paper that answers the following question:
Is a main sequence star an example of a system in equilibrium? If it is not, then explain why not; if it is, then identify the opposing forces or processes that operate inside the star.

4. Review and assess student papers and assess student understanding of concept material.

#### Assessments

Use the Equilibrium System Rubric and the Stellar Equilibrium Rubric provided in the attached file to assess student understanding.

The following questions may also be used to assess student understanding.

1. Consider a book resting on a desktop. The book is said to be at equilibrium. Why is this true?
a. The gravity is greater than the the opposing force of the desk.
b. The gravity is less than the opposing force of the desk.
c. The gravity is equal to the opposing force of the desk.
d. The gravity is not related to the opposing force of the desk.

(Answer c: All forces are equal.)

2. Consider a flying rocket. Which of these statements is true?
a. The rocket moves because it is in equilibrium.
b. The rocket moves because it is not in equilibrium.
c. The force of the rocket thrust is equal to the gravity.
d. The force of the gravity is greater than the rocket thrust.

(Answer b: Thrust is greater than gravity; the system is not at equilibrium.)

3. A star may contract and expand as it develops and eventually dies. What explains this observation?
a. Forces of gravity and nuclear fusion are in equilibrium.
b. Forces of mass and gravity are not in equilibrium.
c. Forces of gravity and fusion are not in equilibrium.
d. Forces of fusion and magnetism are in equilibrium.

(Answer c: Gravity fights against the outward force of fusion. Eventually gravity wins and the star contracts. When fusion begins again, the star expands.)

Self-Reflection:
Describe one human activity that could alter the equilibrium that exists in our natural environment. What new equilibrium would result if this human activity continues? What would be the consequences of this change in the environment?

#### Extensions

Enhancement:
Describe the processes that our sun will follow over the next several billion years.