# Quantitative Conservation of Energy, Part 1

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## Objective

Students will be able quantitatively apply the law of conservation of energy to various situations.

#### Big Idea

Students use their knowledge of conservation of energy quantitatively.

## Work, Power & Energy Quiz

20 minutes

The goal of this lesson is to allow students to have an opportunity to communicate what they have learned about work, power and energy with a formative quiz. Then I want students to take a look at conservation of energy quantitatively to be able to solve for different variables at various points of a specific situation. Since students have already learned about conservation of energy qualitatively, today they develop a model (SP2) for the conservation of energy quantitatively (HS-PS3-1) and use computational thinking (SP5) to solve problems.

To start out class, students take the Unit 5 Work, Power & Energy Quiz. This quiz shows if the students know how to choose which equation to use based on the information in the problem. I like to do this quiz in addition to the different checkpoints that students take along the way so that I can see what they have learned from the checkpoints as well as to see if they can figure out which equation to use for each problem when they are all together. I grade this quiz and return it to them the next class.

## Roller Coaster Example

20 minutes

After the quiz, I ask students to turn to the Conservation of Energy Roller Coaster Problem in their packets. I do this problem with students as guided notes for quantitative conservation of energy. I really like this problem because it shows students multiple points in the same situation and requires them to solve for different things in each section. I model how I think through this problem so that when they are problem solving, they can use a similar thought process.

To start, I ask students what information I have at point 1. Since they know height and mass, they determine they can find the gravitational potential energy at point 1. After solving for potential energy, they identify that point 1 is the highest point and I remind them that at the highest point you have all potential energy. Then, we determine that the potential energy at the highest point is equal to the total mechanical energy of the system since the cart starts at rest at the top of the coaster and kinetic energy is zero. Since we are dealing with conservation of energy, students recognize that the total energy will be the same at each point, it will just be transferred from one type of energy to another.

After we have finished point 1, I ask students to look at the information and determine which point we should do next. Students typically choose to go to point 2 next because it is similar to what they just did, so I ask them to find the potential energy on their own. Then, I ask students how we can find the kinetic energy if we know the total energy from point 1 and just found the potential energy. Students remember back to the video that TE = KE + PE, so all they have to do is subtract to find the kinetic energy. After finding kinetic energy, students should be able to solve for velocity on their own. I let them work and check with students when they are finished.

Students then usually choose to work on point 4 next because it has information given in the picture. I ask them to identify which type of energy they can solve for first and they find it is kinetic energy. The solve for kinetic energy on their own and then I ask them how they can find potential energy if they don't have height. They respond with subtracting the two energies. Once they have the correct potential energy I have them solve for height.

Finally, we look at point 3, which for students doesn't seem like there is a lot of information but they forget that it is at the bottom of the coaster so height is 0 meters. Then students see that since potential energy will be zero, the kinetic energy will equal the total energy. Then students can solve for the velocity on their own.

This problem is very important because it models what students will be doing in their final roller coaster project when they build them at the end of the unit for a summative grade.

## Quantitative Energy Problem Set

30 minutes

After we have finished with the very detailed example about the roller coaster, I ask students to work with their table partners to complete the Quantitative Conservation of Energy Problem WS. They have about 30 minutes to work (until the end of the class period), which should give them enough time to finish most of it; whatever they do not finish is homework. I like students to work in groups for this activity because it can sometimes be difficult to complete the quantitative conservation of energy problems. With groups, they can persevere through the problems as a group instead of feeling defeated trying them on their own. I walk around to make sure I am available for any general questions when students are working. Students are able to finish most of the worksheet in class. The groups that work diligently tend to complete the worksheet in class.