Lab #1: Determining Experimental Acceleration through Motion Detector and Video Analysis

Purpose

The purpose of this experiment is to compare the experimental accelerations of gravity obtained through the LoggerPro Motion Detector and the Vernier Video Analysis.

Procedure

I. LoggerPro Motion Detector

1) Obtained clamps, a metal rod, LoggerPro motion detector, connection cables, a laptop with LoggerPro application, and a basketball.

2) Clamped metal rod to the edge of the desk and clamped motion detector to pole 

around 1 ft away from the edge of the table facing downward. 

3) Connected motion detector to laptop via connection cables.

4) Calibrated motion detector according to Prof. Mason's lab instructions.

5) Reversed direction of data taking in LoggerPro and zeroed at the floor.

6) Collected data while dropping the ball around 6 inches from the detector. Data collected in a table and translated into a Position vs. Time and Velocity vs. Time graph.

7) Applied Curve fit to Position vs. Time graph and Linear fit to Velocity vs. Time graph.  

7) Repeated until sufficient data was obtained (seen in results below). 

II. Vernier Video Analysis

1) Set up my phone on a tripod with a blank wall in frame 

2)  Placed a meter stick in frame.

3) Dropped a ball while recording

4) Imported video onto Vernier Video Analysis

5) Traced movement of the ball as it drops

6) Set scale using meter stick as reference

Results 

Motion Detector Results

    After applying a curve fit to the Position vs. Time graph, it can be observed that A=-4.694 from the Ax^2 +Bx +C equation. We can express this fit as the kinematic equation:

So, the following calculations were performed to obtain the experimental acceleration of gravity, a.

Therefore, a=-9.634 from the position vs. time graph

Additionally, using the linear fit from the velocity vs. time graph, m=-9.630 from the equation y=mx+b. We can express as:

Therefore, a=-9.630 from the velocity vs. time graph.

Uncertainty Analysis

Therefore, the measured acceleration from the motion detector is -9.646 +/- 0.0215 m/s^2.
 

Video Analysis Results

 

To obtain the acceleration, I repeated the calculations identical to the motion detector results. From there, I got a=-9.60m/s^2 from the position vs. time graph and a=-9.497m/s^2 from the velocity vs. time graph.

Uncertainty Analysis

Therefore, the measured acceleration is -9.120 +/- 0.482 m/s^2.

Measurement Variability

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

The measurements agree with the motion detector but not the video analysis. 

What measurements have uncertainty when using the motion detector?

The measurements of uncertainty in regards to the motion detector are position and time.

What measurements have uncertainty when using video analysis?

The measurements that have uncertainty for the video are the position of the camera, position of the ball, time.

Estimate the uncertainty for each of the measurements in the first and second experiments.
I estimate the uncertainty to be around 0.05 for the motion detector since I predict a higher order of uncertainty. I predict the uncertainty for the video analysis would be higher around 0.5 to account for the error.

Use the techniques discussed today to do uncertainty propagation for your measurements. 

Do the measurements agree within your estimated uncertainty?

My measurements agree with those of the motion detector but not for the video analysis.

Which of the measurements is more useful and why? 

The motion detector is more useful since it has a smaller uncertainty and is precisely and accurately measured compared to the video analysis measurements that use a camera, which includes many other measurements that include much larger uncertainties.