# Push Harder — Newton's Second Law

## Summary

## Overview

Don't just teach your students about Newton's laws of motion using diagrams in a textbook—try something hands-on! In this project, students will build their own cars using craft materials and explore the relationship between force, mass, and acceleration. Students can graph data and make observations in real-time using a mobile phone and a sensor app or use a low-tech approach with a meter stick and stopwatch.## Learning Objectives

- Understand the relationship between force, mass, and acceleration as described by Newton's second law of motion.

## NGSS Alignment

This lesson helps students prepare for these Next Generation Science Standards Performance Expectations:- MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object.

Science & Engineering Practices | Disciplinary Core Ideas | Crosscutting Concepts | |||

Science & Engineering Practices | Planning and Carrying Out Investigations. Plan an investigation individually and collaboratively, and in the design: identify independent and dependent variables and controls, what tools are needed to do the gathering, how measurements will be recorded, and how many data are needed to support a claim. |
Disciplinary Core Ideas | PS2.A: Forces and Motion. The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. |
Crosscutting Concepts | Patterns. Graphs, charts, and images can be used to identify patterns in data. |

## Materials

Assorted craft materials for students to build cars:

- Frame/body parts (plastic bottles, corrugated cardboard, popsicle sticks, etc.)
- Round objects to use as wheels (CDs, bottle caps, empty tape rolls, etc.)
- Items to make axles (e.g. a wooden skewer inserted through a straw, or a pencil inserted through a rolled tube of paper)
- Other classroom/office supplies (paper clips, binder clips, zip ties, rubber bands, etc.)
- Tape/glue
- Scissors
- Optional: hobby knives (useful for poking holes in bottle caps to make wheels, adult supervision recommended)

Materials to measure the cars' motion. Which materials you need depends on how you want to do the lesson. See the Explore section for an explanation of the different options.

- Smartphone with a sensor app such as phyphox, available for free on Google Play for Android devices (version 4.0 or newer) or from the App Store for iOS devices (iOS 9.0 or newer). Used to measure the car's acceleration.
- Optional (if you do not want to use a sensor app): tape measure or meter stick and stopwatch. Used to measure total distance the car travels and calculate average velocity.

## Background Information for Teachers

*This section contains a quick review for teachers of the science and concepts covered in this lesson.*

Newton's second law of motion states that the net **force** on an object is equal to the object's **mass** times its **acceleration**. In equation form

**Equation 1:**

*F*is the net force in newtons (N)*m*is the mass in kilograms (kg)*a*is the acceleration in meters per second squared (m/s^{2})

This equation shows, mathematically, what will happen if you change one of the variables. For example, if you double the force on an object and its mass stays constant, its acceleration will also double (Figure 1). If you keep the force constant and double an object's mass, its acceleration will decrease by half.

**Figure 1.**If you increase the net force acting on an object (blue arrow) and its mass remains constant, then its acceleration will also increase (black arrow).

In this lesson plan, your students will build and push their own toy cars, then gather experimental data to understand how changing the force on an object while keeping its mass constant affects its acceleration. This will allow them to see the relationship without needing to understand algebra and Equation 1. However, to do this experimentally, we need a way to measure acceleration. Acceleration is defined as the rate of change of an object's **velocity**:

**Equation 2:**

*a*is the acceleration in meters per second squared (m/s^{2})*Δv*is the change in velocity in meters per second (m/s)*Δt*is the change in time in seconds (s)

So how could you measure acceleration, for example, when pushing a toy car across the floor? You would need to know the car's velocity at two different points, and the time it takes it to travel between those points. This is a little easier if the car starts from resting (so you know the initial velocity is zero), and you measure the velocity after you push the car. You also need to measure the time it takes the car to travel from its starting position to the point where you measure its velocity (Figure 2). Then, you can calculate the car's acceleration using Equation 2.

**Figure 2.**Measurements you need to take to calculate the car's acceleration.

In theory, you could take these measurements using a meter stick and a stopwatch, but in practice this can be difficult to do because our reaction time introduces measurement error. Another approach is to measure acceleration directly using an **accelerometer**. Accelerometers are electronic sensors that are used in many modern electronic devices, like smartphones and video game controllers, to measure motion. Specific sensor apps allow you to easily record data from an accelerometer on your phone. You can mount a phone equipped with the app to a car, and record acceleration when you push the car. Figure 3 shows data recorded for light, medium, and hard pushes while keeping the car's mass constant.

A graph that measures the acceleration of a car being pushed with varying forces has three lines colored red, blue and green. The three plots follow a similar pattern of increasing drastically in the beginning and then decreasing drastically before leveling off. The red line on the graph represents a car being pushed forward with the largest force and has the largest spike in acceleration. The green line on the graph represents a car being pushed with a medium force and has the second highest spike in acceleration. The blue line on the graph represents the car being pushed with the smallest force and has the lowest spike in acceleration.

**Figure 3.**Data recorded using a sensor app on a phone mounted to a toy car. Note that the data is somewhat "noisy" instead of smooth. This is normal, as the car's motion may not be completely smooth, and the app has a limited sampling rate (the number of sensor readings it can take per second), resulting in the "spiky" appearance of the data.

In Figure 3, we can initially see a large positive acceleration when the car is pushed (its velocity rapidly increases). Then there is a small negative acceleration as **friction** gradually slows the car down to a stop (its velocity slowly decreases back to zero). If we graph the maximum acceleration vs. the strength of the force (Figure 4), then we can clearly see the relationship predicted by Equation 1 (if mass stays constant, then when force goes up, acceleration goes up). If you want to calculate the net force acting on the car, you can do so using Equation 1 (first you will need to measure the car's mass).

**Figure 4.**The maximum accelerations from Figure 3 plotted against force strength.

**Note:**the Next Generation Science Standards (NGSS) avoid using the word "acceleration" at the middle school level, instead opting for the phrase "change in motion." While this lesson plan uses "acceleration" throughout, you can decide what terminology to use with your students based on the standards in place for your school district.