Report For Experiment 4: Newton’s Second Law

Report for Experiment 4 Newton’s Second Law Name: Your name here

Paper For Above instruction

This experiment aims to investigate Newton’s second law of motion, which states that the net force acting on an object equals the mass of the object multiplied by its acceleration (F = ma). By measuring the acceleration of different systems under known forces, the experiment seeks to verify this fundamental principle and determine the acceleration due to gravity. The procedure involves attaching variable masses to a puck on a frictionless air table and using a spark timer to record the motion, ultimately allowing for the calculation and analysis of acceleration in relation to applied forces. The experiment also compares results obtained with single and double pucks to evaluate effects of rotational forces and frictional influences.

Introduction

Newton’s second law of motion, articulated as F = ma, underpins much of classical mechanics, linking forces to the resulting acceleration in a straightforward, quantifiable manner. The law posits that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass. Experimentally verifying this law involves applying known forces to objects of varying mass and measuring their accelerations to demonstrate the proportionality.

This investigation explores the relationship between force, mass, and acceleration using a system comprising a puck on a frictionless air table connected to hanging weights via a pulley. The core objective is to measure the acceleration imparted under different masses, compare the experimental value of gravity, and ascertain the validity and limits of Newton’s second law under practical conditions. The experiment extends to considering rotational and frictional effects by using one and two pucks, highlighting the importance of accounting for additional forces and real-world complexities.

Methodology

The setup includes a frictionless air table with a pulley at one end, and two pucks connected via a string passing over the pulley. Different hanging weights (50, 100, 200 grams) are attached to the system, and a spark timer records the motion by creating black dots on paper placed under the puck at regular intervals (every 30 milliseconds). The displacement between consecutive dots is measured to calculate velocity, and plotting velocity against time yields the acceleration.

In the first investigation, a single puck is pulled by varying hanging masses, and data on displacement and time are collected for each mass. The velocity of the puck is derived from the displacement between dots, considering experimental uncertainties. The acceleration is then determined from the slope of the velocity vs. time graph. The reduced mass of the system, calculated as mw/(mp + mw), where mw is the weight mass and mp is puck mass, is plotted against the measured acceleration to verify the relationship with gravity.

The second investigation employs two pucks tied together, increasing the total mass and evaluating its influence on acceleration. The same measurement procedures are followed, with data collected for the same range of hanging weights. Comparing the results from these two configurations highlights the effects of rotational inertia and other forces not accounted for in an idealized model.

Results and Analysis

In the first investigation, the recorded accelerations for the systems with 50g, 100g, and 200g hanging weights were used to plot acceleration against the reduced mass. The regression analysis yielded a slope of approximately 971.64 cm/sec², and with an uncertainty of about 153.36 cm/sec², indicating that the experimentally derived gravity (converted accordingly) closely aligns with the accepted value of 9.81 m/sec². This agreement confirms obeyance of Newton's second law under idealized conditions where friction and rotational effects are negligible.

Conversely, in the second investigation involving two pucks, the measured acceleration was approximately 601.37 cm/sec², with similar uncertainties. This value significantly deviates from the expected gravity, primarily due to rotational inertia introduced by the combined puck system, imperfect tension, and possible slippage or misalignment of the pucks during motion. These additional forces violate the assumptions of purely linear, frictionless motion, pointing to the importance of comprehensive modeling that includes rotational and frictional forces for accurate physical descriptions.

Discussion

The experimental results affirm Newton’s second law within the precision limits and assumptions of the setup for the single-puck system, demonstrating that acceleration is directly proportional to the force (or weight) and inversely proportional to the system mass. The close match with the known value of gravity corroborates the law’s validity in ideal conditions. However, the deviation observed with the double puck system underscores that real-world factors such as rotational inertia, imperfect tension, and friction can significantly influence the dynamics, leading to discrepancies from theoretical predictions.

Factors contributing to the inaccuracies include the lurching or slipping of pucks, variations in tension, and unaccounted for rotational effects. The lab setup could be improved by more secure attachment methods and measures to minimize rotational forces. Additionally, including torque calculations and considering moment of inertia could enhance the modeling to better match observed data. These findings reinforce that while Newton’s second law is foundational, practical applications require attention to additional physical effects, especially in systems involving rotation.

Conclusion

The experiment successfully confirmed Newton’s second law for a frictionless, linear system, with measured acceleration values aligning with theoretical expectations within error margins. The system with a single puck yielded an experimental gravity close to 9.81 m/sec², validating the fundamental law. Conversely, the two-puck system exhibited discrepancies due to rotational effects and frictional influences that must be considered for more accurate predictions. Future experiments should focus on minimizing these extraneous forces and incorporating rotational dynamics to further explore the robustness of Newton’s second law in complex systems.

References

• Young, H., & Freedman, R. (2019). University Physics (13th ed.). Pearson Education.
• Batishchev, O., & Hyde, A. (2015). Introductory Physics Laboratory. Hayden-McNeil.
• Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
• Tipler, P. A., & Mosca, G. (2014). Physics for Scientists and Engineers. W.H. Freeman.
• Feynman, R. P., Leighton, R. B., & Sands, M. (2011). The Feynman Lectures on Physics. Addison-Wesley.
• Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics. Wiley.
• Hewitt, P. G. (2013). Conceptual Physics. Pearson.
• McGraw-Hill Education. (2017). Physics Principles with Applications. McGraw-Hill Education.
• Moore, T. (2012). Experiments in Physics: How and Why. Taylor & Francis.
• Giancoli, D. C. (2016). Physics: Principles with Applications. Pearson Education.