# Pushing the Pathfinder

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## Objective

Students use a bathroom scale and F=ma to determine the mass of my SUV.

#### Big Idea

The mass of an object can be determined by applying a net force to it and measuring its acceleration.

## Context and Supplies

I often get stuck in my thinking that I am limited to using what is in the classroom when doing physics. However, there is a great big world out there just screaming to be measured and observed. In this lesson, I get the students out of their seats and we go outside to build on what we have learned so far. Students use F=ma, take friction into account, incorporate the kinematic equations and use several measuring devices to determine the mass of my SUV.

Over the course of this lesson, students apply Math Practice 1 and make sense of a multistep problem and persevere to solve it. Students use a bathroom scale to push my Pathfinder. Reading the value on the scale and calculating the acceleration, they can calculate the mass. This requires multiple science practices, including Science Practice 5 Using mathematics and computational thinking and Science Practice 6 Constructing explanations (for science) and designing solutions (for engineering). However, Science Practice 3 is the primary standard they use when they plan and carry out an investigations. All of this is done in the context of NGSS Performance Standard HS-PS2-1, the mathematical relationship between the net force acting on an object and its acceleration.

I prepare the following supplies from my classroom:

• Bathroom scale
• Stop watches
• Meter stick or other long measuring device

This is an involved activity and it is done over the course of a 90 minute lab period.

## Challenge Delivered

20 minutes

To kick off this challenge, I have the Mission Impossible Theme music playing. I then display the first slide of the Mass of SUV Activity Power Point. In my best mission impossible voice, I tell the students their mission is to determine the mass of my SUV. The supplies they have to accomplish this mission are a stop watch, measuring tape, the Newton's 2nd Law, the kinematic equations and... a bathroom scale! I hold it up to be dramatic, because no one thinks a bathroom scale can be used to weight a car. The message "self-destructs" and I display the next slide which is a summary of the challenge.

This is a complex task with several steps to get to the solution. For this reason I like to use co-operative learning. I break the class into heterogeneous groups of 3. I choose the groups ahead of time and then post them on the white board. I make my choice of group members using data such as current grade. The reason for heterogeneous groups is that this is a difficult exercise that encompasses much of what we have learned so far, so I want at least one person in each group who can comprehend the steps involved and be able to explain it to the others.

Students have 15 minutes to think through this mission with the supplies at their disposal. While students are discussing a possible solution with their group members, I walk around the room and answer questions and may even provide guidance depending on the group. I have two bathroom scales to pass around. I allow students to hold the scale because they can push on the scale in different ways and realize that they can do more than just stand on it to get a mass or force value. They also realize that they cannot drive the car on the scale as it does not register masses greater than 200 kilograms.

There are classes I have which do not have the physics acumen to work through this activity and come up with a solution. For those classes, I give Finding the mass of a Car Using a Bathroom Scale worksheet. I don't like to do this because students often develop tunnel vision as they work through the questions and they never get the big picture.

## Students Share Their Plan

20 minutes

After a student group creates their plans, they show it to me. If there are problems or missing details then I send them back to fix their plan. I choose the first group that brings me a completed and valid plan to run the experiment. (The plan must include free-body diagrams, details on how the data is to be collected, what calculations should be made and take into account frictional forces.) This group then explains their solution to the class and this plan is used by all groups when they collect the data outside.

The group receives 5 minutes to organize their thoughts so that they can clearly present their solution. That group explains their solution to the class on the white board while the rest of the groups take notes on the plan. They show FBDs and explain how the investigation proceeds. In order to involve the rest of the class, they choose one person from each group to be the data takers (2-3 students to measure length and 2-3 students to measure time) as well as the person who pushes the SUV. All remaining group members record the data so they can complete the write-up after the data are collected. Students are given 5 more minutes to organize their data tables; we then we go outside.

It is essential that the person who pushes the car practices with the scale against the wall. When he or she pushes the car he or she must be able to apply a constant force for both situations. If the scale jumps around, I tell the students that the data are not valid.

## Pushing the Pathfinder

20 minutes

We do this experiment on the large sidewalk in front of the school. It is a level surface with high visibility. A student does the push, SUV Push Video, other students collect the data and I steer the car while it is turned off and in neutral.

The following conditions are required:

• The push is on level ground
• Students are out of the path of traffic (they are focused on this task and don't pay attention to their surroundings)
• We do multiple trials
• Little or no foot traffic is in the area
• My car windows are open so I can communicate with the students
• The student's push is entirely horizontal

First students collect data with the car being pushed at constant velocity. This is the frictional force used for the net force calculation. Then students measure out a distance, 10-15 meters is typical. Starting from rest, the pusher applies a constant force (which is recorded) over the predetermined distance. Three students measure the time it takes to travel that distance. This is enough information to determine the acceleration of the car. Once we have run 5 trials we return to the room to share and analyze the data that were collected.

## Students Analyze the Data

25 minutes

The last slide of Mass of SUV Activity gives what is required for the write-up. Using the collected data, each group has 25 minutes to calculate and analyze their results and complete the report. Each group is to have a write-up.  While students finish their reports in their groups, I circulate the room and give support where needed. I also check to make sure that all the groups have the correct data.

Just before class ends, I reveal the actual mass of my Pathfinder on the board. (The curb weight of all vehicles is written on the frame at drivers door).  I then ask students to calculate the percent difference between their calculation and the actual mass of the car. Since all groups have the same data, they should have similar calculations for mass, with variations arising from rounding differences. I collect this report for grading as the students leave class.