General Physics with Calculus I Laboratory (Mechanics)

Course Description

PHY2048L – General Physics with Calculus I Laboratory is a 1-credit, laboratory-only course that provides the hands-on experimental component of the calculus-based physics sequence required for engineering, physics, and mathematics majors. Students conduct experiments covering the topics studied in the companion lecture course PHY2048 (Physics with Calculus I): kinematics, vectors, dynamics (Newton's laws), work and energy, momentum and collisions, rotational motion and torque, oscillatory motion (simple harmonic motion), gravitation, fluid dynamics, and waves. Students collect and analyze experimental data using algebra, geometry, and calculus, and prepare formal experiment reports that develop scientific writing competence.

The course sits within the Florida Statewide Course Numbering System (SCNS) under Physical Sciences > Physics and is offered at approximately 28 Florida public institutions. PHY2048L is structured as a standalone laboratory course — distinct from the integrated lecture-and-lab format of PHY2048C, which combines lecture and laboratory in a single 4- or 5-credit course. Students whose institution offers the standalone laboratory typically take PHY2048 (lecture, 3 credits) and PHY2048L (lab, 1 credit) concurrently or in sequence. The combined credit of PHY2048 + PHY2048L equals the integrated PHY2048C.

This is the first laboratory course in the calculus-based physics sequence required for engineering, physics, mathematics, computer engineering, and most STEM majors. The algebra-based equivalent for pre-health and biological sciences majors is PHY2053L; students should confirm with their advisor which sequence is appropriate for their major.

Learning Outcomes

Required Outcomes

Upon successful completion of PHY2048L, students will be able to:

• Apply the scientific method in laboratory contexts: hypothesis formulation, experimental design, controls, data collection, analysis, and conclusions.
• Use standard laboratory instruments: digital and analog meters, photogates and motion sensors, force sensors, accelerometers, dynamics carts and tracks, oscilloscopes, balances, and mechanical apparatus.
• Apply calculus-based kinematics and dynamics in experimental analysis (derivatives for velocity and acceleration; integrals for displacement and work).
• Conduct experiments verifying Newton's laws of motion, including measurements of force, mass, and acceleration on dynamics tracks and inclined planes.
• Conduct experiments demonstrating conservation of energy and momentum, including elastic and inelastic collisions.
• Conduct experiments on rotational motion, including measurement of moment of inertia, torque, and rotational kinematics.
• Conduct experiments on simple harmonic motion and waves: spring-mass and pendulum systems; standing waves on strings; sound waves and beat phenomena.
• Apply statistical analysis of experimental data: mean, standard deviation, error propagation, linear regression, and assessment of fit between theory and experiment.
• Construct and interpret graphs of physical quantities using both manual and computer-based methods (Excel, Logger Pro, Capstone, or equivalent).
• Prepare formal laboratory reports in standard scientific format: introduction, theory, methods, data, analysis, conclusions, and references.
• Demonstrate laboratory safety practices, including proper use of equipment and awareness of mechanical, electrical, and ergonomic hazards.

Optional Outcomes

Depending on instructor and institutional emphasis, students may also:

• Use computer-based data acquisition systems (Vernier Logger Pro, PASCO Capstone) for high-precision measurement.
• Apply video-analysis techniques to motion problems.
• Investigate fluid dynamics experimentally (Pascal's principle, Bernoulli's equation, viscosity).
• Conduct open-ended or inquiry-based laboratory exercises in addition to standard verification labs.
• Use uncertainty propagation at an advanced level (partial-derivative methods).

Major Topics

Required Topics

• Measurement and Uncertainty: Significant figures; systematic vs. random error; propagation of uncertainty; the difference between accuracy and precision.
• Kinematics: One-dimensional motion (constant velocity, constant acceleration, free fall); two-dimensional motion (projectile motion); use of motion sensors and photogates.
• Vectors: Vector addition and decomposition; force-table experiments (where used).
• Newton's Laws of Motion: Force, mass, and acceleration on dynamics tracks; Atwood's machine; inclined planes; friction.
• Work, Energy, and Power: Conservation of mechanical energy; the work-energy theorem; energy in spring-mass systems.
• Momentum and Collisions: Impulse and momentum; conservation of linear momentum; elastic and inelastic collisions on tracks or air tables.
• Rotational Motion: Angular kinematics; moment of inertia; torque and angular acceleration; conservation of angular momentum.
• Oscillations and Simple Harmonic Motion: Spring-mass system; the simple pendulum; the physical pendulum; period and frequency measurements.
• Waves: Standing waves on a string; sound waves; resonance and beat phenomena; the speed of sound.
• Data Analysis and Graphing: Linearization techniques; linear regression and least-squares fitting; chi-squared and goodness-of-fit (where applicable).
• Formal Laboratory Report Writing: Standard sections (introduction, theory, methods, results, discussion, conclusion); proper figure and table presentation; uncertainty reporting.

Optional Topics

• Fluid Mechanics: Buoyancy, viscosity, Bernoulli's principle.
• Thermodynamics (Introductory): Thermal expansion, calorimetry, gas laws — included at some institutions.
• Computer-Based Data Acquisition: Vernier or PASCO probe-ware; advanced graphing and analysis.
• Video Analysis: Tracker software for motion analysis from recorded video.
• Open-Ended Inquiry Projects: Student-designed experiments on a chosen topic.

Resources & Tools

• Lab manuals: Most institutions use a custom lab manual or commercial alternatives. Common commercial choices include lab manuals from Pearson, Cengage, or Hayden-McNeil. Many Florida institutions have moved to free, instructor-generated lab packets.
• Companion lecture textbook (recommended): University Physics with Modern Physics by Young and Freedman (Pearson); Physics for Scientists and Engineers by Serway and Jewett (Cengage); Fundamentals of Physics by Halliday, Resnick, and Walker (Wiley); OpenStax University Physics Volume 1 (free, increasingly adopted as a zero-textbook-cost option).
• Laboratory equipment: Dynamics carts and tracks; pulleys and Atwood's machines; air tables; spring-mass systems; pendulum apparatus; rotational motion apparatus; tuning forks and resonance tubes; standing-wave demonstrations; photogates, motion sensors, force sensors; digital balances and timers.
• Data analysis software: Vernier Logger Pro; PASCO Capstone; Microsoft Excel or Google Sheets; LabVIEW (advanced); Python or Matlab for advanced sections.
• Open simulation resources: PhET Interactive Simulations (University of Colorado, free) — used widely as supplements.
• Reference standards: American Association of Physics Teachers (AAPT) guidelines for laboratory instruction.

Career Pathways

PHY2048L is a foundational laboratory course on the way to engineering, physics, and STEM-major careers. Florida-relevant career pathways supported by the calculus-based physics sequence include:

• Engineer — civil, mechanical, electrical, aerospace, computer, biomedical, environmental, materials, industrial. Florida's aerospace and defense industries (the Space Coast: Kennedy Space Center, Cape Canaveral, Patrick SFB; defense contractors L3Harris, Lockheed Martin, Northrop Grumman, Boeing) are major employers.
• Physicist — research, applied physics, optics, semiconductors. Florida programs at UF, FSU (with the National High Magnetic Field Laboratory), USF, UCF (with CREOL — Center for Research and Education in Optics and Lasers), and FAU.
• Computer Engineer / Software Engineer — Tampa Bay, Miami, and Orlando are growing tech hubs.
• Aerospace Engineer — Kennedy Space Center; Lockheed Martin Space; Boeing; SpaceX; Blue Origin.
• Mathematics Educator (secondary) — pathway through Florida math/physics education BS degrees.
• Engineering Technologist — Florida College System AS degrees in engineering technology.

Special Information

Articulation and Transfer

PHY2048L is part of the Florida common course numbering system and articulates seamlessly to all SUS institutions. The combination of PHY2048 (3 cr) + PHY2048L (1 cr) is equivalent to the integrated PHY2048C (4 cr) at institutions that offer the latter format. SUS engineering and physics programs accept either combination.

Calculus-Based vs. Algebra-Based Physics

Critical distinction: PHY2048L is the calculus-based laboratory required for engineering, physics, mathematics, computer engineering, and similar STEM majors. The algebra-based equivalent is PHY2053L, taken alongside PHY2053 (lecture). Students must know which sequence is required for their major:

• Engineering, physics, mathematics, computer engineering → calculus-based: PHY2048/PHY2048L (or PHY2048C) and PHY2049/PHY2049L (or PHY2049C).
• Pre-health, biological sciences, agricultural sciences → algebra-based: PHY2053/PHY2053L (or PHY2053C) and PHY2054/PHY2054L (or PHY2054C).

The calculus-based sequence is more rigorous; the algebra-based sequence does not satisfy engineering or physics-major requirements at any SUS institution.

Prerequisites and Co-requisites

Most Florida institutions list PHY2048L as having a prerequisite or co-requisite of MAC2311 (Calculus I) or higher mathematics, and as a co-requisite of PHY2048 (the lecture course). PHY2048L generally cannot be taken without taking PHY2048 either previously or simultaneously. Specific policies vary by institution; check your institution's catalog.

Course Format and Workload

PHY2048L typically meets once per week for 2–3 hours. Expect 8–12 experiments across the semester, each requiring pre-lab preparation (reading the lab handout, completing pre-lab problems) and post-lab analysis (formal report writing). Out-of-class workload is typically 3–5 hours per week, with much of that devoted to lab-report writing.

Position in the STEM Curriculum

PHY2048L is the prerequisite or co-requisite for PHY2049L (General Physics with Calculus II Laboratory), which covers electricity, magnetism, and optics. Together they form the year-long calculus-based physics laboratory sequence required for engineering and physics degrees.

Course Code Variations

Florida institutions consistently use PHY2048L for this course. Titles vary slightly: "Physics with Calculus I Laboratory," "General Physics with Calculus I Lab," "Physics Laboratory for Engineers and Scientists I," and "General Physics Using Calculus I Laboratory" all refer to the same SCNS course. Honors variants (PHY2048L_H or similar) exist at some institutions for high-achieving students.