Lab Report

Objective:

To determine the acceleration due to gravity g by analyzing the free fall of an object using video analysis and ImageJ software.

Materials:

• 5g weight

• Ruler (30 cm or longer)

• Webcam

• Computer with ImageJ software installed

Experimental Procedure:

1. Set up the Equipment:

   • Verify all the materials.

   • Place the webcam at a fixed position to capture the free fall of the object from different heights (e.g., 0.27 m, 0.25 m, 0.23 m, and 0.20 m).

2. Record the Free Fall:

   • Drop the object from the designated heights and record each drop using the webcam.

   • Ensure the video captures the entire fall, from release to impact.

3. Analyze the Videos Using ImageJ:

   • Import the recorded videos into ImageJ.

   • Track the object's position frame-by-frame and note the height at each time step.

   • Generate data for time vs height from the video.

4. Plot the Data:

   • Plot two graphs:

     • Time vs Height

     • Time squared t² vs Height

   • Use the slope of the t² vs Height graph to calculate the gravitational acceleration g.

5. Compare Results:

   • Compare your calculated g value with the theoretical value g=9.81 m/s².

   • Compute the percentage error.

Data Table (For Students to Fill Out):

Questions for Discussion:

1. What factors might have affected the accuracy of your results?

2. How would including air resistance alter your results?

3. How could you improve this experiment in future trials?

Instructions:

1. Analyze the recorded videos of the free-fall experiment using ImageJ.

2. Create graphs for Time vs Height and Time Squared vs Height.

3. Use the data to calculate the value of g and compare it with the theoretical value.

4. Submit a report with the following sections:

   • Introduction: Describe the purpose of the experiment and the theory of free fall.

   • Procedure: Detail the steps you took to perform the experiment and analyze the data.

   • Data: Present the tables and graphs of your findings.

   • Analysis: Calculate g and compare it to the theoretical value, including percentage error.

   • Conclusion: Discuss your results and any potential sources of error.

Problem 1: Basic Free Fall Calculation

An object is dropped from a height of 10 m. Assuming there is no air resistance, calculate the time it takes for the object to reach the ground and the velocity at the point of impact.

Problem 2: Effect of Air Resistance

 Given a 5g spherical object with a diameter of 4.5 cm and a drag coefficient Cd=0.47, calculate the terminal velocity. How would this affect the time it takes to reach the ground when dropped from a height of 10 m?

Problem 3: Experimental Analysis

 In a free fall experiment, a ball was dropped from a height of 0.3 m and was found to take 0.25 seconds to hit the ground. Use this data to calculate the acceleration due to gravity g. Compare it with the theoretical value g=9.81 m/s².

Problem 4: Error Analysis

 In a series of free fall experiments, a student measured the following times for drops from 0.25 m: 0.22 s, 0.24 s, and 0.23 s. Calculate the average time and use it to determine g. What is the percentage error compared to the theoretical value?

Problem 5: Graphical Analysis

Plot the height vs time squared for the following data obtained from a free fall experiment:

• Height: 0.30 m, 0.25 m, 0.20 m, 0.15 m, 0.10 m

• Time squared: 0.09 s², 0.07 s², 0.05 s², 0.03 s², 0.01 s² Using the slope of the graph, calculate the acceleration due to gravity.

1. Worksheet (40%): Completeness and accuracy of theory, calculations, and explanations.

2. Assignment (30%): Detailed report, correct use of formulas, analysis, and discussion of results.

3. Problem Set (30%): Correctness of solutions, step-by-step calculations, and proper explanation.

Each lab group should download the Lab Report Template and fill in the relevant information as you experiment. Each group member should answer the Worksheet, Assignment, and Problem individually. Since each lab group will turn in an electronic copy of the lab report, rename the lab report template file. The naming convention is:

[Short Experiment Number]-[Student ID].PDF

Submit the Lab Report in PDf format