# Understanding the Work Energy Theorem: In the lab or as lecture demonstration

### This activity has benefited from input through a review and suggestion process.

This activity has benefited from input from faculty educators beyond the author through a review and suggestion process as a part of an activity development workshop. Workshop participants were provided with a set of criteria against which they evaluated each others' activities. For information about the criteria used for this review, see http://serc.carleton.edu/sp/compadre/devactivities/reviewcriteria.html.

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

#### Summary

While this laboratory activity is a verification lab until the very last step, it allows students to visualize and understand the relationships between the variables, and deepen their understanding of work, begun with a series of concept questions in the previous lecture meeting. This could also be done as a lecture demonstration if necessary, with the questions framed as in-class discussion questions. The discrepant event and the lab design that appears in the last part add the opportunity for real laboratory exploration.

## Learning Goals

The goal of this activity and the questions asked of the students is to develop a conceptual understanding of work and to strengthen students' basic understanding of what an integral in calculus actually "means". The pre-lab questions probe common misconceptions about work and sloppiness about defining systems that can get students into trouble in more complicated problems. Students must come to an understanding of what they are measuring, and trouble shoot to figure out what possible approximations or sources of error impact their measurements, and how they impact them. The open-ended opportunity to improve the activity at the end encourages students to think carefully about the experimental design and the relationships between the variables.

## Context for Use

Ideally, this is taught in a lab setting, with students coming to class having done the pre-lab questions.

The class then opens with a discussion of the answers to these questions, often uncovering a common mistake, using gravitational potential energy when the earth is external to the system.

The students should already be familiar with forces and have done the Atwood's machine as a demonstration or a lab (we do it as a demonstration, asking students to predict what will happen as we vary the masses, then as a source of questions for small-group problem-solving work). In their lab groups (usually 3 students) the students work through the questions.

In this lab, the procedure is given to them, so there is not much freedom unless the students do the optional redesign at the end. However, the primary purpose of the lab is to get the students to the representations of the data to allow them to explore those and improve their understanding. Since this is the case, it is possible to do this activity as an in-class lecture demonstration, although this would require reformatting the questions, and eliminate the chance for the students to actually test their improvements to the activity, although they could still discuss them.

The class following this would explore work in various systems in more detail and in more quantitative, complicated, problems.

## Description and Teaching Materials

The activity as a lab activity is included, along with the solutions version. It is written for the Pasco PASPORT data-acquisition system.

This lab activity or lecture demonstration requires a computer and a computer-based data-acquisition system. It can be adapted to other systems.

Student Version of Activity (Acrobat (PDF) 55kB Jul17 07)
Solutions version of Activity (Acrobat (PDF) 71kB Jul17 07)

## Teaching Notes and Tips

It is very important that teaching assistants, if used, be well-prepared. They must not only thoroughly understand the material, but be prepared NOT to answer the students' questions too directly. Discussion of the type of questions you might ask the students to help lead them to find the answers on their own is important.

## Assessment

Students must come to class prepared, and be engaged in the in-class activity. Peer instruction has proven to be an effective tool for engaging students.

Qualitative as well as quantitative questions on both work and understanding of integrals are asked in homework and exams.