Lab 4: Investigating Newton’s Second Law Using An Air Track ✓ Solved

Lab 4: Investigating Newton’s Second Law using an Air Track

The goal of this lab is to investigate how changing the distribution of the total mass on a rider with a hanging mass on an air track will lead you to verify Newton’s second law, without friction. You will first calculate the theoretical acceleration as you move mass from the “rider” to the “bucket” and graph your predicted results of F_net = m_tota in Excel. Then, measure the acceleration indirectly by timing the rider passing between two photogates, and graph your measured Force as a function of acceleration, comparing with your predicted graph. The external force in this setup is from the hanging mass’s weight, which accelerates both itself and the rider along the air track. Assuming full air blast, friction is negligible.

Pre-lab Analysis

Complete this section before coming to lab.

1. Draw free body diagrams with all forces acting on each mass, to be copied into your lab notebook.
2. Answer these questions and include the responses in your lab notebook and report:
   • What is the net external force causing the system to accelerate?
   • What is the total mass of the system?
   • What is the formula for acceleration based on m₁, m₂, and g?
   • Predict:
     • As m₁ approaches infinity, what does acceleration approach?
     • As m₂ approaches infinity, what does acceleration approach?

Getting Started in the Lab

Define the total mass on top as m₁ and the hanging mass as m₂. The initial rider (rider + flag + hooks) should be weighed; similarly, weigh the empty bucket. Start with initial conditions: no extra mass, with the rider and bucket weighed. Include 50 grams initially on top, then transfer 10 grams at a time from the rider to the bucket, maintaining a constant total mass. Calculate the predicted acceleration for each configuration using the formula a = m₂ g / (m₁ + m₂), repeating for different mass distributions as per the table. Use error propagation techniques to account for measurement uncertainties.

Constructing Predicted Graphs

Calculate predicted accelerations and plot F_net versus acceleration in Excel using scatter plots with trend lines and equations. The slope of this line represents the mass of the system, confirming Newton’s second law (F_net = m_tota). Include error bars based on uncertainty estimates. Print and paste the predicted graph into your lab notebook for comparison.

Running the Experiment

Set system with initial mass, ensuring the string length prevents the bucket from hitting the floor. Position photogates before and after a measured distance Δx, and ensure they remain at fixed positions for all trials. Conduct multiple runs for each mass distribution, recording time Δt for the rider passing the gates. Repeat for each mass transfer (from initial setup to full transfer of 50 grams), performing six trials each, and calculating the average and standard deviation for the timing data.

Compute acceleration from timing data using a = 2Δx / t². Identify main sources of error, including timing uncertainties and measurement inaccuracies. Use error propagation to estimate the uncertainties in acceleration. Plot the experimental F_external versus calculated acceleration in Excel, adding trend lines and equations for comparison against theoretical predictions.

Analysis and Comparison

Compare the predicted and experimental values by plotting both data sets on the same graph with distinct symbols, adding trend lines. Determine if discrepancies are within experimental uncertainties. Discuss potential sources of error, including random errors like timing variations and systematic errors such as friction or misalignment. Identify that a major systematic error here might be residual friction, which can affect acceleration measurements.

Conclusion

Summarize whether your experimental results support Newton’s second law under the conditions tested. Consider the effects of measurement uncertainties and systematic errors, and propose improvements for more accurate results in future experiments.

References

• Serway, R. A., & Jewett, J. W. (2018). Principles of Physics. Cengage Learning.
• Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics. Wiley.
• Cutnell, J. D., & Johnson, K. W. (2019). Physics. Wiley.
• Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers. W. H. Freeman.
• Giancoli, D. C. (2013). Physics: Principles with Applications. Pearson.
• Young, H. D., & Freedman, R. A. (2019). University Physics with Modern Physics. Pearson.
• NASA Glenn Research Center. (2013). Newton’s Laws of Motion. NASA.
• OpenStax. (2016). Physics. Rice University. https://openstax.org/details/books/physics
• Blackboard Course Materials. (2023). Online course notes and error analysis tutorials.
• Lab Manual for Physics Experiments. (2022). Department of Physics, [Your Institution].