Experiment 3: Acceleration
Student: Virgil Smith
Date Performed: 14 Feb 12; 1800-hours
Phy111-C11
Section 1: Experiment and Observation
A. Objective
This experiment will provide data to calculate the acceleration of a marble as it rolls down an incline plane over measured periods of time. To do this, the marble’s velocity will be determined and then its acceleration. This will allow comparison with the conclusion reached by Galileo in the 1600’s.
B. Equipment used
• Labpaq manual
• Computer with 2003 word
• 3 meter measuring tape with millimeter graduations
• 2 meter piece of corner trim
• Masking tape
• Angle locater tool
• Chair
• Marble
• Stopwatch
• Bucket
C. Data
Data table 1 records the 5 trials made at each of 3 different distances indicating, time (seconds), distance (meters), and calculations for velocity (m/s), acceleration (m/s²) and standard deviation (m/s²).
Data Table 1
Height of ramp = .90 m Angle of Incline = 16˚
Trial No. / Distance (m) / Time (s) / Velocity (m/s) / Acceleration (m/s²)1 / .50 / .81 / 1.23 / 1.52
2 / .50 / .84 / 1.19 / 1.42
3 / .50 / .87 / 1.15 / 1.32
4 / .50 / .85 / 1.18 / 1.39
5 / .50 / .84 / 1.19 / 1.42
average / .84 / 1.19 / 1.41
σ / .022 / .029 / .072
1 / 1.00 / 1.15 / 1.74 / 1.51
2 / 1.00 / 1.22 / 1.64 / 1.34
3 / 1.00 / 1.16 / 1.72 / 1.48
4 / 1.00 / 1.13 / 1.77 / 1.57
5 / 1.00 / 1.19 / 1.68 / 1.41
average / 1.17 / 1.71 / 1.46
σ / .035 / .051 / .089
1 / 1.50 / 1.44 / 2.08 / 1.44
2 / 1.50 / 1.47 / 2.04 / 1.39
3 / 1.50 / 1.44 / 2.08 / 1.44
4 / 1.50 / 1.47 / 2.04 / 1.39
5 / 1.50 / 1.45 / 2.07 / 1.43
average / 1.45 / 2.06 / 1.42
σ / .014 / .021 / .023
acceleration overall σ = .026
Section 2: Analysis
A. Calculations
The average and standard deviation values were calculated for each of time, velocity and acceleration. Velocity was determined by using the measured distance (tape measure) and time (stop watch) values.
Velocity was figured first by use of the base formula: s=(Δv)t where s equal the measured distance, Δv is velocity change, and t is time recorded on the stopwatch Since the initial velocity is zero, Δv is the just stated as v and is solved as v=2s/t. For example, the determined velocity for trial 1 for a distance of .50 meters is v=1.00m/.81s=1.23m/s.
Having solved for velocity, acceleration can now be determined by the base formula: v=at, or a=v/t. For example, the determined acceleration for trial 1 with a distance of .50 m and velocity of 1.23 m/s is a=(1.23m/s)/.81s =1.52 m/s²
B. Error Analysis
The error analysis for this experiment was the standard deviation, which measures the variance of the determined acceleration values from the average acceleration value. The standard deviation (σ) for the average acceleration of the three different distances of this experiment was .026 m/s². This is an overall uncertainty range of 1.43 ± 0.026 m/s².
Section 3: Discussions and Conclusions
A. Discussion
One can only imagine Galileo devising an experiment like this that could very well disprove the teaching of the day: that objects fell at a speed based on their weight. He didn’t have stopwatch accuracy, but still managed to shake things up in his quest for a confirmable truth. While the accuracy of his trials in this area may have been in question, the precision obtained by probably numerous trials was no doubt a “Eureka moment” for him. He demonstrated by rolling a ball down an incline that acceleration depended not on an object’s weight, but on its angle of incline, and that it did remain constant for a specific angle. He also confirmed that velocity increased over time in the mathematical relation of: s=(at²)/2, with s=distance, a=acceleration and t=time. The results of this experiment are in agreement with his conclusions.
B. Results
I did do a few practice rolls before actually recording any times. It was difficult to anticipate and click the stopwatch at the exact time the marble passed the marked line on the incline. The friction of the wood corner trim should have remained constant throughout the trials, so should have had minimal effect on the determination of the acceleration under these particular circumstances. The minimal air resistance also remained constant. That would leave only the force of gravity acting on the marble. This simple experiment was very effective in confirming the constant acceleration of a marble rolling down an incline. As the incline increases, more care may be needed to click on the actual time that the marble passes the marked distances on the incline.
C. Interpretation of Results
The far right column of data table 1 indicates the determined experimental values that we wish to compare and reach a conclusion. The standard deviation calculated by comparing the three average acceleration values from the three different distances indicates that it is reasonable to conclude that the marble has a constant acceleration as it travels down the inclined plane (1.43 ± 0.026 m/s² at an incline angle of 16˚). That constant acceleration is also indicated by the increasing velocity of the marble down the incline. I believe it is reasonable to conclude that the rate of acceleration of the marble would increase with the angle of the incline, being a new constant for each angle. This would be true until the incline reached vertical, at which time the marble would be at maximum acceleration, or free fall.
D. Errors – Sources and Why
The raw data gathered in most any experiment, particularly those that involve the human factor, most certainly will contain areas of uncertainty.
For example, the fastest I can click the stopwatch on and off is 0.15 second. We can “anticipate” when to click the stopwatch, but that part of the data is definitely compromised by the human factor. Even though the incline angle was relatively small (16˚), the marble still was a challenge to catch at the exact moment it passed the distances. In my first calculation of the velocities I neglected to multiply the distances by a factor of 2 as indicated in the formula used. I did; however, catch this. It did remind me of the absolute importance of attention to duty. The corner trim I used was very straight, but it was not so for other pieces in my garage. An incline with a dip or rise would definitely throw off the data. I used an angle indicator that I have used in measurement of cones and pits in grain bins in my job as a loss adjuster. I checked the angle at various positions up and down the incline to confirm its value. Random errors could have affected the end results of this experiment.