## Summary

Svenja Lohner, PhD, Science Buddies

## Overview

Students explore how force, mass, and acceleration are related in this hands-on lesson plan. By experimenting with pushing a box across the table while varying force and mass and measuring the box's acceleration with a mobile phone and a sensor app, students discover Newton's second law of motion for themselves.

## 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:- HS-PS2-1. Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.

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

Science & Engineering Practices | Analyzing and Interpreting Data.
Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution.
Using Mathematics and Computational Thinking. Use mathematical representations of phenomena to describe explanations. |
Disciplinary Core Ideas | PS2.A: Forces and Motion.
Newton's second law accurately predicts changes in the motion of macroscopic objects. |
Crosscutting Concepts | Cause and Effect. Empirical evidence is required to differentiate between cause and correlation and make claims about specific causes and effects. |

## Materials

Materials per group of 4 students:

- Push/pull spring scale, available from Amazon.com
- Small plastic box that fits the mobile device.
**Note**: the box should be sturdy and not bend when force is applied with the spring scale. If it deforms, the applied force is not fully transferred to the box, which will affect the data. - Scale for measuring mass (can be shared by the whole class)
- Weights (2 x 200 grams)
- Tape
- 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).

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## 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 tells us that the net force acting on an object is equal to the object's mass times its acceleration. Mathematically, this can be expressed as the famous equation:

**Equation 1:**

- F is the force in newtons [N]
- m is the mass in kilograms [kg]
- a is the acceleration in meters per second squared [m/s
^{2}]

It is important to remember that in this equation, F is the *net*, or total, force acting on the object. The classic high school physics example used to demonstrate this is a box subject to an applied force while sliding on the floor, as shown in Figure 1.

**Figure 1.**A free-body diagram of a box being pushed across the floor. The positive x axis points to the right and the positive y axis points up.

This box is subject to four forces:

- The applied force F
_{app}, which acts in the positive x direction (to the right) - The frictional force F
_{f}, which acts opposite the direction of motion (so, assuming the box is already moving to the right, it acts to the left, in the negative x direction) - Its own weight, W, which acts in the negative y direction (downward)
- The normal force, N, from the floor pushing up on the box, which acts in the positive y direction (upward). Assuming the floor is flat, the normal force is exactly equal and opposite to the box's weight.

We can apply Newton's second law to the x and y axes individually. In this lesson we will only look at forces in the x direction. Using F_{x} to represent the net force in the x direction, analyzing the free body diagram gives:

**Equation 2:**

In this lesson, your students will apply a known force (F_{app}) to a box of known mass using a spring scale. The box will contain a mobile device equipped with a sensor app. The app can use the device's built-in accelerometer to measure acceleration directly.

If you assume friction is negligible (e.g. the box is sliding on a smooth surface), this process lets your students measure all three values in equation 2. They can then plot their data and compare their experimental results to what is predicted theoretically by Newton's second law. Do they see a linear relationship between force, mass, and acceleration?