Introductory Mechanics Course Research Articles

Investigating the Effects of Cognitive Style on the Motivation of Students Enrolled in a Team-Based Learning Formatted Agricultural Mechanics Course at Louisiana State University

Educators have a plethora of teaching methods that allow them to tailor the learning environment to meet students’ needs. One novel instructional approach that has grown in popularity in U.S. higher education has been the flipped classroom approach, which has become a popular way to embrace a student-centered learning environment. Of the various types of flipped classrooms, team-based learning allows students to learn content outside of classroom time and spend more time doing hands-on activities as a team in a laboratory environment. This study aimed to describe the effect of cognitive style on the motivation of undergraduate students enrolled in an introductory agricultural mechanics course at Louisiana State University. Descriptive statistics, including means, frequencies, and standard deviations, were utilized to test the hypothesis and gain a holistic understanding of the data. We also conducted a Mann-Whitney U test to determine if a statistically significant difference existed between motivation and cognitive style. No statistically significant differences were found between cognitive style and motivation. However, the more innovative students in this investigation had higher motivation scores than those identified as more adaptive.

Force and motion misconceptions in Moroccan high school science majors: insights from video game activity

ABSTRACT This study delves into the misconceptions about force and motion prevalent among Moroccan high school science major students. It meticulously analyzes the impact of videogame activity on the formation and persistence of these misconceptions. A cohort of 234 students, who underwent remote introductory mechanics courses, were involved in the study. Alongside the use of the revised Force Concept Inventory for investigating misconceptions, we employed cluster sampling and a descriptive survey to concurrently explore students’ year-long experiences with various videogames. The findings indicate that a substantial part students exhibit non-Newtonian conceptual understanding of force and motion. Interestingly, highly engaged videogame players consistently demonstrated a shift in their misconceptions’ nature. No statistically significant correlations were found with grade, age, or gender, except for videogame spending time frequency. This research underscores the importance of mechanics reasoning, especially among digital natives and avid gamers. These insights not only pave the way for robust Digital Game-Based Learning tools to identify and rectify misconceptions, but also provide a catalyst for further exploration in this field and its broader implications.

Tripping on the Moon

Two recent lunar lander missions have toppled over on touchdown. We analyse a simplified model to determine the lateral speed of an object that results in tipping, as a practical example of an inelastic collision that conserves angular momentum. The solution employs rotational dynamics and conservation laws covered in an introductory mechanics course. We suggest further investigations, including simple experiments that can be performed in the teaching laboratory.

Cables of a prescribed length under concentrated or distributed loads

A general analysis of inextensible perfectly flexible cables of negligible weight and a prescribed length, loaded by an arbitrary number of concentrated loads, or by a uniformly distributed load per unit horizontal length, is presented. A catenary cable under its own weight, with or without a concentrated force, is also considered. The sags under loads and tensions in all segments of the cable are determined. The results are derived in closed-form, apart from a numerical solution of a single nonlinear algebraic equation for a suitably introduced parameter in the last step of the analysis. The study complements the treatment of cables under concentrated forces available in undergraduate textbooks, which omit the consideration of cables whose length is prescribed in advance. The general analysis may be found appealing for a senior or graduate structural mechanics course, while its specialization to cables with two or three loads only is well suited for an introductory mechanics course. Expressions for a catenary cable subjected to a concentrated load at its midpoint are also derived, with only one nonlinear transcendental equation for the introduced load parameter needing to be solved numerically. Three student projects are suggested which address the existence and uniqueness of the cable configuration under a concentrated force with a specified sag and length of the cable, the lifting of two symmetrically hung loads by an upward force, and the determination of the deformed shape and tension in a catenary cable subjected to a concentrated force at an arbitrary point of the cable.

Smartphone-based undergraduate research projects in an introductory mechanics course

At the University of Göttingen, we implemented undergraduate research projects into a first-year mechanics course for physics majors and teacher-training students. Our primary goal was to foster students’ affective factors and higher-order thinking skills in a self-directed, crosslinking, inquiry-based learning setting. A total of 160 students were organized into 40 small groups which worked on one of six open-ended experimental tasks, utilizing smartphone sensors for flexible first-hand data collection outside laboratories. The tasks originate from the Erasmus+ project DigiPhysLab and were significantly modified and opened to be used for undergraduate research projects. In this manuscript, we present the underlying rationales behind this program, outline the core concepts behind the developed experimental tasks, and explain the actual implementation. Additionally, we offer insights into the assessment process for the project work, including the evaluation of scientific posters and responses to eight reflection questions. To facilitate this, we have employed two rubrics to ensure a comprehensive evaluation process.

Extensions to the theorems of Pappus to determine the centroids of solids and surfaces of revolution

Extensions to the first and second theorems of Pappus are presented, whereby the centroid of a surface or solid of revolution can be determined using only the geometric properties of the generating plane curve or figure and the arc of revolution. The derivations are well suited to first-year-level courses in mathematics and engineering. From a didactic perspective, the resulting formulas are simple to apply, especially since the required geometric properties are typically available in standard tables of plane sections or relatively routine to derive. Furthermore, the formulas provide a general scaffold for students to attempt problems involving axisymmetric bodies while also reinforcing and embedding their knowledge of the properties of the generating plane shapes. A selection of illustrative problems is discussed that are generally regarded to be challenging for introductory mechanics courses but for which the formulas derived in this article provide straightforward solutions.

Nonlinear oscillations for beginners. Calculating period using an elementary computational approach

Determining the period of a nonlinear oscillation is a challenging task that requires a strong mathematical background in solving nonlinear differential equations. However, the procedure can be significantly simplified using the area under the 1/|υ|= f(x) graph, where υ is the velocity of the oscillating object and x is its displacement from its equilibrium position. The proposed method requires elementary computational tools and is appropriate for determining the period of any nonlinear undamped oscillation. Characteristic examples are presented, such as the simple pendulum, the oscillation with a power-law restoring force, and the cubic-quintic Duffing oscillator. The proposed approach provides accurate results and is appropriate for introductory physics and mechanics courses.

The rotational rocket

A rotational rocket is the angular analogue of the familiar translational rocket. It spins about an axis fixed in position, as a result of the ejection of matter (typically in the form of one or more fluid jets) tangentially from its rim. Examples include a rotary lawn sprinkler, Hero’s engine, or a carousel off of which balls are thrown. The thrust equation is developed starting from Newton’s second law for rotations. Special cases that could be used in class or homework in an introductory mechanics course are discussed.

Using a Simple Pendulum to Calculate the Distance Between Two Train Stations

In this article, we demonstrate the use of a simple pendulum to explore the concepts of kinematics and dynamics. A simple homemade pendulum and a phone-based accelerometer are used to determine, at various points in time, the acceleration of a moving train. The dynamical and kinematics data from the homemade pendulum and the accelerator can then be compared, and this in turn highlights the relationship between dynamical and kinematics quantities. This project is originally part of a coursework requirement assigned to the first four authors for their introductory classical mechanics course at a university in the summer of 2020. Similar ideas have been explored earlier independent of this work, but this work will focus on the detailed description of our approach and using updated technologies as our benchmark. The project is one that can be implemented readily as an activity in high school physics classes.

Development and didactic analysis of smartphone-based experimental exercises for the smart physics lab

Smartphone-based experimental exercises were incorporated as part of the homework problems in an introductory mechanics course at a university. A quasi-experimental field study with two cohorts design was performed to measure the impact of such exercises on motivation, interest and conceptual understanding. The empirical results on learning achievement show a significant positive influence of the smartphone-based experimental exercise for the dynamics of rigid bodies topic with a medium effect size of d = 0.42. For the analysis of rotational motion topic, a positive learning achievement for both groups was evidenced, but the effect size of the smartphone-based exercise was rather small at d = 0.20 . The intrinsic and germane cognitive loads turned out to be similar at an intermediate level for both groups. However, the extrinsic cognitive load for the intervention group decreased significantly, which might be the reason why more complex experimental exercises foster conceptual understanding.

On the operation of the Hanstead car

We consider the operation of the hypothetical mechanical vehicle driven by an engine powered by small rockets introduced by P D Hanstead in the inaugural volume of this journal. Hanstead arrived at three contradictory conclusions regarding the change in velocity should some of the rockets malfunction at a particular time. This thought experiment constitutes an excellent, conceptual discussion, or even exam, question for an introductory mechanics course.

Pendulum: the partial and global approach

The pendulum was an important scientific instrument in the 17th century. It became a typical textbook problem in the 18th century. After the introduction of vectors in physics in the 1890s, the pendulum problem started to be progressively solved in the manner we know nowadays from introductory mechanics courses. Starting from F = ma and using the tangential component of weight, we arrive at the equation of motion. The other part of F = ma, which concerns the weight radial component, tension and centripetal force, has in no way deserved the same attention from textbook writers, if any. Physics education research has, however, pointed out relevant aspects of the phenomenon related with the latter part of the equation. The present paper presents an experiment, which reflects those relevant aspects, and provides a mathematical insight into the phenomenon suitable for the high school student.

TiltTray: A 3D-Printed Apparatus to Teach Inclined-Plane Physics Through Smartphone Portrait-Landscape Transitions

Today’s students are increasingly immersed in a landscape of screens and handheld digital devices through which a good deal of their interactions with the world around them are mediated. Physics educators, meanwhile, continue to rely on traditional human interactions with the physical world, such as sliding down a ramp or throwing a baseball, in order to illustrate fundamental concepts in physics. Regrettably, these interactions are decreasingly representative of the kinds of everyday activities that our students engage in, reducing their degree of engagement with the material. A new opportunity lies in the behavior of smartphones in response to sustained tilted orientations, which has for some time become a familiar mechanism of interaction between students and many of the mobile apps that they engage with on a daily basis. Here we demonstrate how a methodical investigation of this digital-era mechanism can be used to introduce the inclined plane, a standard topic in most introductory mechanics courses. We also present an open-source 3D-printed apparatus designed to support this investigation and the experiences from well over 1000 students in three different colleges.

The Covid-19 shutdown: when studying turns digital, students want more structure

In March 2020, universities in Norway and many other countries shut down due to the Covid-19 pandemic. The students lost access to classrooms, libraries, study halls, and laboratories. Studying turned digital. Because it is unclear when this pandemic will cease to affect students and because we cannot know whether or when a new pandemic occurs, we need to find ways to improve digital study-life for students. An important step in this direction is to understand the students’ experiences and perspectives regarding how the digitalization affected their study-life both in structured learning arenas and their self-study. Therefore, we interviewed 12 students in an introductory mechanics course at a Norwegian university in June of 2020. Through a thematic analysis, we identified four broad categories in the students’ different experiences and reflections, namely that digitalization: (a) provides benefits, e.g. the flexibility inherent in online video lectures; (b) incurs learning costs, e.g. students reducing their study effort; (c) incurs social costs, e.g. missing being around other students; and (d) increases the need for structure, e.g. wanting to be arranged in digital groups to solve mandatory tasks. We also found that the 2019 students on average scored significantly better on the final exam than the 2020 students, d = 0.31, but we discuss why this result should be interpreted with caution. We provide suggestions for how to adapt courses to make students’ digital studying more socially stimulating and effective. Furthermore, this study is a contribution to the historical documentation of the Covid-19 pandemic.

ArduinoTM microprocessors as a platform for modeling framework labs

Modeling is an essential skill for the career physical scientist or engineer. One approach that attempts to integrate this element of critical thinking into the laboratory environment is the modeling framework lab. In this style of lab exercise, students construct a model of both the measurement apparatus and the phenomenon under investigation. A key challenge to implementing this approach in introductory mechanics courses is that the use of electronic data acquisition modules obfuscates the process by which primary measurements are made and interpreted. Conversely, the use of simple analog devices does not adequately prepare students for scientific investigations in the “real world.” Here, the ArduinoTM microprocessor is considered as a platform to bridge this pedagogical gap. Student survey data regarding perceived value of the labs, force concept inventory testing, and analysis of final exam scores were used to assess the efficacy of this approach. Results from this style of lab were compared to “task-measurement” style labs, in which students followed a set of instructions and utilized commercial “black box” data acquisition tools. ArduinoTM-based modeling framework labs showed robust increases in both perceived and measured quantitative skills compared to “task-measurement”-taught sections. These data support the use of open-source microprocessors as a powerful pedagogical platform for offering modeling framework labs in introductory mechanics.

‘Forced to think’—an analysis of how students benefit from online warm-up exercises with feedback

Active learning yields better learning outcomes than traditional, lecture-based teaching. Common approaches in large lecture courses are activating elements during the lectures and warm-up activities using online learning environments. However, implementing warm-up exercises, on which students work on by themselves makes formative feedback increasingly important. We have studied students’ views on warm-up online exercises, focusing on the role of automated feedback. We compared two types of feedback: feedback which guided the student towards the correct answer and feedback that guided the student towards the correct reading materials. We have also examined the correlation between students’ views on the exercises and learning outcomes, as measured by exercise and exam points. The exercises were administered with a Moodle-based system focusing on teaching and assessment using a computer-based algebra kernel. The study was conducted during the first introductory mechanics course in physics at the University of Helsinki. We concluded that the preferred type of feedback was dependent on the student, i.e. different students prefer different kinds of feedback. Importantly, the students who completed the exercises alone reported benefiting more from them, which shows that the warm-up exercises successfully extended support for students outside of classroom hours.

Derivation of the differential continuity equation in an introductory engineering fluid mechanics course

The differential continuity equation is elegantly derived in advanced fluid mechanics textbooks using the divergence theorem of Gauss, where the surface integral of the mass flux flowing out of a finite control volume is replaced by the volume integral of the divergence of the mass flux within the control volume. To avoid the need for introducing the Gauss divergence theorem in an introductory fluid mechanics course, introductory textbooks in fluid mechanics have opted to use a more simple approach, which depends on the consideration of an infinitesimal control volume and the use of Taylor series expansion. This approach, however, involves a first order truncation of the Taylor series expansion and the use of approximate equality signs which may imply to undergraduate students that the derived continuity equation is an approximate equation. The present study proposes an alternative derivation of the differential continuity equation using a finite control volume and is based on the simple concept of the antiderivative function and the fundamental theorem of calculus. The proposed derivation eliminates the need to formally introduce the Gauss divergence theorem in an introductory engineering fluid mechanics course while avoiding the use of truncated Taylor series expansion and approximate equality signs, hence providing a more simple and sound understanding of the derivation of the differential continuity equation to undergraduate engineering students.

Bead on a uniformly rotating rod: why does the bead move out if there is no force in the radial direction?

Problems involving rotating systems analysed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. In this article we try to see what could be the factors that lead to this difficulty and propose a set of arguments that could be used to resolve the confusion. We take a specific example of a bead sliding without friction on a rotating rod to address the issues involved. After solving the problem in the inertial reference frame by integrating the equations of motion expressed in the plane polar coordinate system, we carry out a consistency check on how the radial motion can be accounted for by the force that the rod exerts on the bead. We hope that going through this exercise would help students to get more comfortable with understanding problems in a similar mould.

Importance of math prerequisites for performance in introductory physics

Previous work has looked at the relationship between high school preparation and student performance in calculus-based introductory mechanics (physics 1) courses. Here, we extend that work to look at performance in introductory calculus-based electricity and magnetism (physics 2), and we look at the significance of what college math courses have been completed in addition to high school preparation. Using multiple linear regression including these measures of prior preparation, we examine the correlation between taking various math courses in college and final exam scores in introductory physics courses at a highly selective west coast university. In physics 1, we find that prior college math coursework is not a predictor of physics 1 final exam score. In physics 2, we find that having taken a course in vector calculus is a strong predictor of physics 2 exam performance (effect size=0.58 standard deviations, p<0.001), even when controlling for students’ physics 1 final exam scores (effect size=0.27 standard deviations, p<0.01). These effect sizes are similar in magnitude to other measures of students’ incoming physics and math preparation. Qualitative analysis of student exams from physics 2 reveal that this “vector calculus gap” is due to differences in reasoning about vectors and geometry and some differences in conceptual understanding of circuits, as vector calculus itself is not required to perform well on the final exam. That is, basic reasoning related to vector calculus appears to be important, but the formalisms of vector calculus do not.Received 10 November 2020Accepted 1 February 2021DOI:https://doi.org/10.1103/PhysRevPhysEducRes.17.010108Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasStudent preparationPhysics Education Research

Impact dynamics for gravity-driven motion of a particle

Introductory mechanics courses use the bouncing ball model to familiarize students with the principles of binary inelastic collisions. Nonetheless, in undergraduate courses, the modeling of binary systems typically disregards the time of contact and the effects of gravity, which yields to a constant coefficient of restitution (COR) and, as a consequence, prevents students from elucidating the real dependence of COR with impact speed. In this work, we proposed a simple experimental setup to investigate the impact dynamics of a spring-mass body that bounces on a rigid plate as well as a theoretical framework that captures the velocity dependence of the COR for low-impact speeds. Our analytical expression for the COR highlights the role-played by gravity, impact speed and collision time on the collision dynamics. Our results suggest that the inclusion of gravity force allows an adequate estimation of the critical impact speed and maximum deformation distance, crucial parameters to differentiate between repulsive and attractive interaction regimes. Our experimental setup enables the clarification of several key concepts of mechanics while it is easy to be performed in most undergraduate laboratories.