Lab #1: Measuring Acceleration and Determining Measurement Variability

Purpose

Using LabPRO and Logger Pro, successfully determine the acceleration of gravity acting on a ball and accurately find the standard deviation of 5 trials with uncertainty. 

Measurment of Acceleration due to gravity from a motion detector

What did you measure?

In this experiment, my group conducted an experiment using a motion detector and LabPRO. The motion detector tracked a basketball falling with the force of gravity acting on it. In the image on the left, there is a motion graph showing the path the ball took. The wave crests represent the high points of the ball, and the wave troughs represent when the ball hits the ground. The top graph represents a position vs. time graph and the bottom graph represents a velocity vs. time graph.

How did you measure?

1. Set up the motion detector on poles to have enough space for the ball to fall uninterrupted underneath the motion detector. 

2. Hold the basketball underneath the motion detector approximately 15 cm before beginning the program to measure.

3. Release the ball and generate the position and velocity vs time graphs.

4. Analyze the data gathered. 

What were your 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 for your results?

Gathering information from 4 other groups, the standard deviation is able to be calculated. Below are the people I was able to gather information from:

Yvette Martinez: -9.63 m/s^2

Hiroshi Matsune: -9.15 m/s^2

Elle Tanjuakio: -9.62 m/s^2

Steven Lee: -9.60 m/s^2

The standard deviation was 0.154 m/s^2 for the 5 data sets.

-9.530 m/s^2 +- 0.154 m/s^2

Measurment of Acceleration due to Gravity from Video Analysis

What did you measure?

In this experiment, I analyzed the motion of a volleyball falling to find the acceleration of gravity. The analysis of the video was done through Logger Pro. Similar to the previous experiment, 2 graphs were produced. A position vs. time graph fitted with a quadratic line and a velocity vs. time graph fitted with a linear line. 

How did you measure?

1. I recorded a video depicting me dropping a volleyball next to a pole the length of 1.55 meters an even distance from the camera. 

2. I uploaded the video to Logger Pro and formatted the video to create an origin at the top of the pole and making the pole the reference length.

3. Every 2 frames, I added points on the top of the volleyball. 

4. I generated a graph with the points from the video.

5. I analyzed the graphs with quadratic and linear lines respectfully.

6. With the data, I found the acceleration due to gravity.

What were your results?

The position vs time graph's quadratic fit was differentiated twice to receive an acceleration of -9.46 m/s^2.

The velocity vs time graph's linear fit was differentiated once to receive an acceleration of -9.38 m/s^2. 

What was the standard deviation for your results?

Gathering information from 4 other scientists, the standard deviation is able to be calculated. Below are the people I was able to gather information from:

Dilay Gedik: -9.812 m/s^2

Oscar Chavez: -9.814 m/s^2

Marcus Mendoza: -9.940 m/s^2

Sam Trieu: -9.418 m/s^2

The standard deviation of the experiments is +- 0.200 m/s^2.

-9.688 m/s^2 +- 0.200 m/s^2

Measurment Variability/Conclusion

% difference between two experiments

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

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

What measurements have uncertainty when using the motion detector?

The measurements that have uncertainty when using the motion detector are the distance, time, and position.

What measurements have uncertainty when using video analysis?

The measurements that have uncertainty when using video analysis are the capability of the camera, the perspective distortion, and the position of points plotted on graph. 

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

I estimate that the uncertainty for the first experiment would be similar to the standard deviation of +- 0.154 m/s^2 and the uncertainty for the second experiment would increase to account for more of the measurements. I believe that it would be close to +- 0.255 m/s^2.

Uncertainty propagation for your measurements.

Do the measurements agree within your estimated uncertainty?

The measurements do not agree within the estimated uncertainty. 

Which of the measurements is more useful and why?

The measurements from the motion detector are more useful because the error created from the motion detector is much less than the video analysis app. The numbers from the motion detector are more precise and have a smaller deviation.