Name: Kevin Nguyen
Lab partners: Jose Rodriquez, Kevin Tran
Date performed: 01-Mar-2017
Purpose: This lab's purpose is to perform an experiment that confirms that the acceleration of a falling object (barring all other external forces except gravity) is 9.8m/s^2.
Theory/Introduction: Our objective was to measure the acceleration, "g", of an object in free fall. In order for us to do so, we used a strip of paper tape that has already been marked and recorded the position of each dot from the 0 - cm mark. We had done this in order to find the position of the falling object at each 1/60th of a second ( 1/60th of a second is relevant because the rate at which the falling object created a spark on the paper is 60 Hz). We also needed the position of the falling object in order to calculate the change in position of the object so that we can find the mid-interval speed by dividing ∆x by 1/60th of a second. We also needed to calculate mid-interval time by dividing each 1/60th of a second by 2 since we used be using mid-interval time and mid-interval speed in order to find the value of g. G was found by first plotting mid-interval time on the x - axis and mid-interval speed on the y - axis. We then found an equation for our line plot. The equation gave us the value of the slope of the line which was our value for g (since acceleration is the slope, or derivative, of velocity).
We also compiled our value of g to the class's values of g and found the standard deviation of the entire class data. The reason why we calculated the standard deviation of the entire class data was so that we can compare our values, as a whole, to the actual value of g, which was 981 cm/s^2.
Summary of apparatus/ experimental procedure: First, we got a strip of marked paper tape shown below to take measurements of.
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| The marks represent the position of the free-falling object every 1/60 seconds. |
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| Using a meter stick, we measured the position of each dot from the 0-cm mark. |
After collecting our data, we followed a series of steps from the lab packet. We entered the data for time, distance (from 0 to the mark), the ∆x, mid-interval time, and mid-interval speed on the excel spreadsheet. We also graphed a distance vs time graph and a mid-interval time vs mid-interval speed graph. We then use line-fit to find the equation of the line of distance vs time graph and mid-interval time vs mid-interval speed graph and found our g-value from the slope of the equation of the mid-interval time vs mid-interval speed graph. We then compared our g value to other group's g value and calculated the standard deviation of the data and compared the class's average g value to the actual value of g.
Measured Data/ Calculated data:
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| We measured the distance and time, highlighted in purple and blue, respectively, and calculated ∆x, mid-interval time and mid-interval speed. |
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| Calculating ∆x |
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| Calculating mid-interval speed |
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| Calculating mid-interval time |
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| Equation of the Mid-interval time vs Mid-interval speed |
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| Equation of the distance vs time graph |
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| Class Data |
This was explained in the Theory/ introduction section.
Conclusions:
Although our value of g was similar to the class's value of g, the average value of g, 961.5 cm/s^2, was much lower than the actual value for g, which was 981 cm/s^2. This error came to be because when the object fell and recorded its position on the paper tape, it was in constant contact with the paper tape, which created friction on the falling object. As a result, friction made the falling object accelerate at a slower rate than 981cm/s^2.
Part 1 Questions:
1.
2. I can get the acceleration due to gravity from my velocity/ time graph by finding the slope of the line. I can do that either by finding the average velocity for a certain time interval or by taking the derivative of any point. In the picture below, I found the acceleration by taking the derivative. The accepted value of g was higher than my value of g.
3. I can get the acceleration due to gravity from my position/ time graph by taking the double derivative of the position line in order to find acceleration. The accepted value of g is higher than my value of g.
1. In our data, we got values that ranged from 950 cm/ s^2 to 965 cm/s^2
2. Our average value is lower than the accepted value of g.
3. The class's values of g tend to be around 950 cm/s^2 to 970 cm/s^2.
4. Our average value of g may be different from the class's values of g because my group or the class may have committed systematic and random errors in our experiment. Systematic error includes
inaccurately measuring each position of the dots by several millimeters. Random error includes measuring different values for the same position of the dot.
5. The purpose for part 2 of the lab was to inform us of how mistakes in measuring and collecting data and inaccuracies of measuring tools may lead to errors and uncertainty of our results. Key ideas include learning how to calculate standard deviation, or a quantity that measures the extent of deviation from a calculated average value, learning about random and systematic errors and how to prevent them, and being mindful to big mistakes such as not accounting for friction in our experiment
. From part 2, we learned how to calculate standard deviation on excel and learning how to minimize systematic/ random errors in our future experiments.
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