Motion Detector/Video Analysis Lab & Write Up

 

Enbo Zhang

Purpose of the LAB

Determine the acceleration of gravity acting on a ball from motion detector and video analysis from Logger, also find the standard deviation of 5 trials with uncertainty

Measurement of acceleration due to gravity from a motion detector.

What did we measure:

    In this experiment, we recorded the position, velocity, and time of a basketball in free fall using a motion detector and LabPRO. The motion detector, set up approximately 1.5 meters above the ground, tracked the ball as it fell under the influence of gravity. The collected data was used to generate position vs. time and velocity vs. time graphs. In the position graph, the peaks represent the highest points the ball reached, while the troughs indicate when it contacted the ground. The velocity graph illustrates the changes in speed throughout the motion. By analyzing these graphs, we gained a better understanding of the ball’s motion and acceleration due to gravity

How did we measure it:

    We used a motion detector to measure the position, velocity, and time of a falling basketball. The detector was mounted on poles approximately 1.5 meters above the ground, ensuring enough space for the ball to fall uninterrupted. The basketball was held about 15–20 centimeters below the detector before starting the measurement program. Once released, the motion detector recorded data to generate position and velocity vs. time graphs. Finally, we analyzed the collected data to study the motion of the falling basketball.

What were our results:

The graphs were analyzed and fitted with a quadratic and linear line respectively

The position vs time graph's quadratic fit was differentiated twice to receive an acceleration of -9.6 m/s^2.

The velocity vs time graph's linear fit was differentiated once to receive an acceleration of -9.65 m/s^2. 

What was the standard deviation of our result:

Data:

Enbo Zhang: -9.65 m/s^2

Dilay Gedik: -9.63 m/s^2

Yvette Martinez: -9.63 m/s^2

Elle Tanjuakio: -9.62 m/s^2

Steven Lee: -9.60 m/s^2

Results:

The standard Deviation was 0.012 m/s^2

by checking the data, it fits 3/5 of the data.

Conclusion:

(-9.63 +/- 0.012) m/s^2

Measurement of acceleration due to gravity from Video Analysis.

What did I measure:

    In this experiment, I recorded the position, velocity, and time of a falling basketball to determine the acceleration due to gravity. The analysis was conducted using Logger Pro, which tracked the ball’s motion as it fell under the influence of gravity through the video. The collected data was used to generate two graphs: a position vs. time graph fitted with a quadratic curve and a velocity vs. time graph fitted with a linear trend line. Then analysis the graph to have a better understanding of the motion of the basketball's free fall.

How did I measure it:

    To analyze the motion of a freely falling basketball, I positioned my recording device at a distance that captured the entire motion while ensuring the camera was parallel to me. To enhance precision, I placed a one-meter-long rolling ruler on the ground as a reference for the scale factor. I then threw the ball upward, allowing it to fall freely. The recorded video was uploaded to a video analysis website, where I adjusted the frame rate to advance every one frame. I marked the center of the ball at the frame where it first left my hands and continued marking its position every other frame until it reached the ground. To ensure accurate measurements, I set the scale system to one meter along the rolling ruler and placed the origin at the top of the ball in the first marked frame, providing a consistent reference point for analysis.

What were my results:

The graphs were analyzed and fitted with a quadratic and linear line respectively

 

The position vs time graph's quadratic fit was differentiated twice to receive an acceleration of -9.28 m/s^2.

The velocity vs time graph's linear fit was differentiated once to receive an acceleration of -9.14 m/s^2. 

What was the standard deviation of my result:

Data:

Enbo Zhang: -9.28 m/s^2

Jose Zavala: -9.46 m/s^2

Mingke Jiang: -9.73 m/s^2

Dilay Gedik: -9.41 m/s^2

Chengxi Yang: -9.20 m/s^2

Results:

The standard Deviation was 0.14 m/s^2

by checking the data, it fits 3/5 of the data.

Conclusion:

(-9.42 +/- 0.14) m/s^2

Write-up on measurement variability.

The % difference between the results of the two experiments.

Do your measurements agree within the uncertainty determined from the standard deviation?

    The measurements from the video analysis agree with the uncertainty determined from the standard deviation, but the measurements from the motion detector do not agree with the uncertainty of the standard deviation.

What measurements have uncertainty when using the motion detector?

Position & Velocity: Errors may arise from sensor resolution, misalignment, and interference affecting accuracy.

Timing: Small delays in the detector’s response can impact time-based calculations.

Reflection Issues: External objects or the ball’s surface may affect signal detection.

What measurements have uncertainty when using video analysis?

Scaling & Perspective: Misalignment of the ruler or camera angle distortion can affect measurements.

Frame Rate Limitations: Motion changes between frames may not be fully captured.

Manual Tracking Errors: Inaccuracies in marking the ball’s center can alter data.

Motion Blur: Fast movement may make position tracking less precise.

Estimate the uncertainty for each of the measurements in the first and second experiments.

From motion detector, it's given estimate uncertainty for velocity is +/- 0.0141m/s

From video analysis website, it's given estimate uncertainty for velocity is +/- 0.07 m/s

Do the measurements agree within your estimated uncertainty?

For motion detector it agrees, 0.012 < 0.014

For video analysis it does not agrees, 0.14 > 0.07

Which of the measurements is more useful and why?

I think overall the motion detector is more useful, first all it has more accuracy then the video analysis one, -9.63 is closer to -9,81 then -9.42 is. Second, it has smaller uncertainty, which means it has more precision. So compare to video analysis result, the results from motion detector is more precise and more accurate. Lastly it also agrees with my estimates uncertainty. As conclusion, the results from motion detector is more useful.