## At a Glance

• Physics

#### Instructional Level

• College & CEGEP

• Mechanics

#### Social Plane(s)

• Group
• Whole Class

• Discussing
• Solving problems
• Creating & designing
• Writing
• Experimenting & conducting inquiry

## Technical Details

#### Useful Technologies

• vehicle and an empty stretch of parking lot

#### Class size

• Small (20-49)

#### Time

Brief segment of class period (< 20 mins)

#### Instructional Purpose

• Exploration & inquiry

#### Socio Affective Engagement

• Collaboration & group work

## Overview

In this activity, students are tasked with measuring the mass of a car using simple tools.

Dividing students into groups of 3-4, the instructor begins with a demonstration using a wheeled chair. The instructor pushes the chair (causing it to accelerate) then releases it (allowing it to decelerate). In their groups, students are to create free body diagrams and equations of motion describing the two stages. The instructor should ensure the students don't forget friction during the acceleration phase.

The instructor then presents a problem: students are to measure the mass of the car. They will have access to several ...

In this activity, students are tasked with measuring the mass of a car using simple tools.

Dividing students into groups of 3-4, the instructor begins with a demonstration using a wheeled chair. The instructor pushes the chair (causing it to accelerate) then releases it (allowing it to decelerate). In their groups, students are to create free body diagrams and equations of motion describing the two stages. The instructor should ensure the students don't forget friction during the acceleration phase.

The instructor then presents a problem: students are to measure the mass of the car. They will have access to several bathroom scales, a stopwatch, and a measuring device (possibly along with other implements such as string which can serve as red herrings). Students discuss how this can be done using their equations of motion, then plan out how they will take their measurements and what parameters they will need, essentially designing an experiment. They need not use the equations of motion they have come up with if they feel they have a better solution; students should feel free to come up with their own experimental designs and be creative.

In an empty stretch of parking lot, the plans are executed using several trial runs. The actual experiments should be done as a class to save time, with students organizing into groups to take on different roles in the experiment and sharing data. Several methods should be attempted, however the "ideal" method is to push the car using the scales, which measures the applied force. Using a constant force, the acceleration can be measured when the force is applied then again after it is released using kinematics (assuming constant acceleration) or by using a ticker tape-style method in which objects such as sandbags are dropped out of the car window at regular intervals. In the second method the acceleration can be found using the slope of a velocity-time graph. They are then left with two equations and two unknowns (the coefficient of friction and the mass).

Working in their original groups, students then use the data they have collected to calculate the mass of the car, then write up a lab report describing their experiment and result.

Note that the downloadable package includes a description of the activity and a student handout, but they differ somewhat from that described here. The original version has been modified by Kevin Lenton for use in his own mechanics course.

## Instructional Objectives

Students learn to apply their knowledge of kinematics and dynamics to real world problems.

Students learn to distinguish inertial mass from gravitational mass, and to solve systems of equations.

Mass of A Car

## Contributor's Notes

Kevin Lenton

Vanier College, Montreal, QC

### Benefits

This activity is motivational, students get into the idea of looking at a real world problem and using physics to solve it, especially since this is a problem that they couldn’t otherwise solve without specialized equipment. They use the equations that they have learned in non-obvious ways, taking something abstract and bringing it into the world.

This activity also hits all the learning objectives for that part of the course: kinematics, Newton’s laws, and equation solving. Unlike a lot of activities, students get to really work with problem solving and equations.

Students can also come up with different ways of solving the problem, which the class can attempt then compare to the “correct” solution.

### Challenges

This activity requires good weather; be careful of what time of year you do this. You may also want to check in with campus security beforehand to let them know what you’ll be doing.

It can be difficult to find enough space to do this activity on campuses (and, of course, you may not have a car).

You should use two or three bathroom scales, but even then it’s very difficult to get a (mostly) constant force. It takes a few runs for students to get used to this, and to understand that they will have to accelerate along with the car to keep a constant force. This can itself be a teaching experience as it demonstrates very intuitively the difference between constant acceleration and constant velocity.

### Tips

If done correctly, answers are typically within about 10% of the correct value.

You can also get students to come up with other ways to measure the mass of the car. Students can be creative, but their methods don’t always work, which presents a great opportunity for teaching. It can be fun to try out several different methods.

It’s also interesting to throw in a few other tools or measurement devices into the mix, forcing students to really think about their choice of tools.

Although it’s technically possible to measure the friction by pushing the car at a constant speed, in practice it is very hard to estimate when the car is moving at a constant speed and therefore does not work well.

Make sure you use some sort of padding between the scale and the surface of the car, for example a towel, to prevent scratches.

You can have students self-organize into teams to take on different roles in the experiment itself. The experiment(s) should be done as a class to save time.