Newton’s Second Law of Motion: Experiment Report

Abstract

This lab report delves into the fundamental principles of Newton's Second Law of Motion, exploring the interplay between mass, acceleration, and force. The primary objective of this experiment is to ascertain how Newton's second law, expressed by the equation F=ma, explains the relationships between mass and acceleration (Part 1) as well as force and acceleration (Part 2). Through a series of trials, we aim to demonstrate that mass and acceleration are inversely proportional, while force and acceleration are directly proportional.

Introduction

Newton's Second Law of Motion, a cornerstone of classical mechanics, postulates that the force acting on an object is directly proportional to the acceleration experienced by that object and inversely proportional to its mass. This relationship is elegantly expressed by the equation F=ma, where F represents force, m stands for mass, and a signifies acceleration. In this experiment, we seek to validate Newton's second law by conducting two distinct parts. In Part 1, we investigate the acceleration and force applied to an object moving on a horizontal plane, while in Part 2, we explore the force and acceleration of a glider connected to a weight via a string on an inclined plane. Our goal is to observe how Newton's second law of motion explains the variation in acceleration for objects in these different scenarios.

Methodology

The central research question in this experiment pertains to the validity of the data obtained in Part 1 and Part 2 to explain Newton's Second Law of Motion. To address this question, we conducted a series of carefully designed procedures and measurements.

Part 1: Horizontal Plane

To investigate the acceleration of a glider on a horizontal plane, we employed a pulley system. A glider connected by a string was used, and the force of gravity acted on a weight suspended from the pulley, causing the glider to move along the frictionless pulley track. Our initial configuration involved a glider with a mass of approximately 100 grams and a hanging mass ranging from 30 to 40 grams. Multiple trials were conducted, systematically decreasing the hanging mass to observe changes in acceleration. To measure acceleration accurately, we utilized a motion detector in conjunction with Logger Pro, a computer program capable of recording and analyzing motion data. Additionally, throughout each trial, we adjusted the weight on the hanger to maintain equilibrium.

Part 2: Inclined Plane

In Part 2, we repeated the same experimental setup as in Part 1, with one crucial alteration—the glider and weight were placed on an inclined surface. To establish a consistent angle of inclination, we ensured that the board remained at a fixed angle throughout Part 2. We utilized Logger Pro to measure the acceleration at two different angles. To vary the angles, we had the option of adjusting the weight on the hanger or adding additional books to the base of the board to create a steeper incline.

The equipment used for this experiment included a computer, Vernier computer interface, Logger Pro software, Vernier motion detector, Pasco air track with accessories, ruler, smart pulley, and thread. These instruments facilitated data collection for both Part 1 and Part 2, enabling us to construct graphs illustrating the relationship between force and acceleration in the subsequent graphical analysis.

Results and Analysis

Upon executing the procedures outlined in Part 1 of our experiment, our group successfully gathered data regarding the acceleration of the lab glider on a horizontal surface. We employed a straightforward formula that involved adding the mass of the glider to the mass of the weight to determine the applied force acting on the system. In addition to measuring the masses of the objects, we calculated the applied force and recorded both theoretical and measured differences for each trial. Our exploration in this part of the experiment enabled us to comprehend the components of force and their relationship to Newton's Second Law by examining the glider's acceleration due to the applied force. However, it is essential to acknowledge potential sources of error, such as possible calibration issues with the Logger Pro software, which could lead to invalid results and hinder our ability to explain the theory of Newton's second law of motion.

In the graphical analysis presented below for Part 1, we observe a linear relationship between force and acceleration. This linear correlation is in accordance with Newton's second law, which is expressed mathematically as a=F/m. As mass is divided by the applied force, the acceleration should increase after each trial, as reflected in our graph.

In Part 2, we applied the same principles as in Part 1 to analyze the data. The key distinction is that Part 2 involved an inclined plane. From our interpretation of the graph, particularly examining the slope and y-intercept, we derived the equation Mwg=(Mw+Mc)-a + Mcg sin(theta). The slope of this equation represents (Mw+Mc)-a, while the y-intercept corresponds to Mcg sin(theta). Through this equation, we deduced that the results in Part 2, when compared to those in Part 1, exhibited a decrease in the measured theoretical values, leading to a substantial increase in the percent difference. Possible sources of error in this table include inaccuracies in setting the inclined plane or measuring its inclination angle, as well as potential miscounts of the glider and weight masses, which could compromise the validity of our data.

Similarly, in Part 2, our group constructed another graph illustrating the inverse proportionality between force and acceleration. As in Part 1, the data collected in Part 2 yielded a linear graph, affirming that this experiment effectively demonstrates Newton's second law of motion. The results reaffirm the validity of Newton's Second Law of Motion, emphasizing the proportional relationship between applied force and acceleration.

Conclusions

Through the completion of this experiment, I have acquired valuable insights into measuring the masses of objects and determining the forces applied to them. Our diligent data collection efforts in both Part 1 and Part 2, aided by Logger Pro, provided us with not only the acceleration values but also theoretical and measured values. Most notably, we successfully constructed graphs in both parts, elucidating the correlation between force and acceleration.

This experiment reinforced the fundamental principles of Newton's Second Law of Motion, demonstrating that the mass of an object is inversely proportional to its acceleration, while the applied force on an object exhibits a direct proportion. Newton's second law of motion finds practical application in everyday scenarios. For instance, as explained in the article "Science Experiment: Newton’s Second Law of Motion" by Fred Bortz, riding a bicycle exemplifies this law in action, where the bicycle represents the mass, and the force applied by one's legs on the pedals leads to acceleration and increased speed.

In conclusion, this experiment has deepened my understanding of Newton's Second Law of Motion, allowing me to apply it to various situations, such as calculating acceleration on different surfaces and determining theoretical, measured, and percent difference values using the second law of motion formula.