Gravity, Energy, and Conservation
Topic/Concept: Gravity, Energy, and Conservation
Prerequisite knowledge required: Since this is an introduction to these concepts, students don’t need much prerequisite knowledge other than some simple mathematics. The TA(s) will organize an outside of class math review so that all the students can be brought to the same level. This math need not extend beyond simple algebra.
Resources required: Students should come prepared with a notebook and a writing utensil in order to take notes and work out problems. The teacher can use the black/white board for my lecture, and the teacher can prepare handouts with various problems to reinforce the material.
Learning Goals: Students will gain the ability to work through simple word problems involving gravity, energy conservation, and planetary orbit. They will also come away with a brief historical introduction to the evolution of the ideas of planetary orbits and the laws of motion.
Learning Objectives: Students will be able to use and understand the components of:
Opening Activity: During the first part of the class, the teacher will need to go through what all of the symbols mean. After that has been presented, the teacher should give a brief history of some of the important names in early physics and astronomy. The teacher and class can go through the revolution of circular orbits to elliptical orbits. When you get to Newton, the teacher can present his laws, and provide a few examples. At Kepler, the teacher can present his laws and provide a few examples. The teacher should also try to find some animations (whether on the computer or on a video) to demonstrate Newton’s and Kepler’s laws. After the historical foundation, the teacher should present the idea of conservation of energy and some of its uses. It may also help to have a few physical demos. Some possible examples:
1. a vacuum tube with a feather and a penny to show that they fall at the same rate demonstrating the constant acceleration due to gravity
2. an air hockey table to demonstrate inertia and equal and opposite reactions
3. a pendulum that returns to the same spot it has been released from to show that it returns to the same spot demonstrating conservations of energy (an interesting variation is a bowling ball pendulum released in front of my face)
4. Kepler’s laws can most easily be demonstrated via a video/computer animation
Concept Activity/Task: The teacher should pass out a worksheet that has a few word problems for the students to work on in groups. These problems will emphasize Newton’s laws, conservation of energy, and Kepler’s laws through math and conceptual interpretations. A few possible example questions:
1. A person is out in space some distance from Earth (given values for all necessary variables). What is the force of gravity that the Earth is pulling on him? What is the force of gravity that he is pulling on the Earth?
2. An elevator is sitting on the 10th floor at rest when its cable breaks. (again given values for variables). Assuming no friction, what will its velocity be when it hits the ground? What was its acceleration?
3. Given the Earth’s period around the Sun, average distance of the Earth from the Sun, and three other planets’ average distances from the Sun, calculate the orbital period for the three other planets.
4. Given a drawing of a planets orbit as an ellipse, when will it be moving the fastest? When will it be moving the slowest?
5. Given a planet’s period, and the mass of the Sun, at what average distance would we expect to find this planet?
This activity should be worked on in groups of three or four. If we have enough time to finish the worksheet, I will ask for volunteers to work out the problems or verbally provide the answers to these problems to the rest of the class. We may discuss the answers if there is are differing opinions.
Checking For Understanding: The teacher should walk around the class while they are working on the handout and try to gauge how well they understand the material. The teacher should offer hints when needed, and answer questions when asked. From their responses to the questions, the teacher can see what concepts the students know, and what need to be reinforced in a future class period. Then if ther is time to present the answers the teacher can further judge how well the material has been absorbed. The teacher may also assign an out of class homework sheet to further measure their understanding.
Assignment: If the class does not finish working on the in class handout, it will be assigned as homework. Students can continue to work in the same groups or find a different group (or work separately if they so desire). If however, there is enough time for the majority of students to finish the in class worksheet and we are able to have students present the answers, I will be ready with a similar homework sheet for them to work on outside of class.
Comments: Note: This learning plan will most likely take a few lectures to get through, and is intended to cover a week of class time.