Daniel Guzman
Alejndro Rodriguez
In this lab, we are trying to see if an object will accelerate at 9.8 m/s^2 when there are no external forces besides gravity.
This sturdy column provides a long 1.5m falling distance for an accurate reading. When the free falling body, held at the top by electromagnet, is released, its fall is precisely recorded by a spark generator on piece of spark-sensitive tape. We do this by turning the spark generator to 60 Hz causing the electromagnet to turn off and the object falling. We then can then find the position of the free falling body by getting the tape and measuring the distance from the origin (or the first tick mark). With this information, we can plot it by velocity vs. time graph and a position vs time graph and thus help us determine the acceleration of the object.
In this lab, we decided to take the first 12 measurements of the position of the free falling object. We are able to determine that the object fell over the course 1 second ( or 60 Hz) because it would leave a mark on the spark-sensitive tape at every 1/60 second (1Hz). We were able to get the position by measuring the distance with a meter stick ( on the centimeter side) from the origin (the first mark on the tape). We got the the change in position value by subtracting the intial value from the final value each time. We are able to get the mid-interval time by dividing the time interval (1/60 s) by 2 and adding that to our initial time value. We were able to find the V interval speed by getting our change in position value and diving that by our time frame of 1/60 second.
This is our position vs. time graph with our change in position value on the y-axis and our mid-interval time on the x-axis. We were able to get the formula of this graph by doing a liner fit on the graph and by displaying the equation and R^2 value.
This is our velocity vs. time graph in which we were able to get with our V interval speed values on the y-axis and our mid-interval time values on the x-axis. We were able to get the formula by first doing a linear fit of the graph and by then displaying the equation and the R^2 value.
Questions/Analysis
1.When you solve for acceleration, you can solve it in two ways, first you get the average velocity and divide that by that time interval, and the second way is to get the velocity at the mid point ( which is the same as the average velocity given the time interval is the same ) and divide that by that time frame.
2. You can get the the acceleration due to gravity from the velocity vs. time graph by taking the 1st derivative of the equation of the graph. Our value is way off as our value is 960 cm/s^2 compared to accepted value of gravity which is 980 cm/s^2.
3. You can get the acceleration due to gravity from the position vs. time graph by taking the 2nd derivative of the equation of the graph. When you take the 2nd derivative of the equation, you get a value of 957.48 cm/s^2 which is off because our accepted value of gravity is still 980 cm/s^2.
The patterns that I see makes sense because the position and velocity would increase with respect to time due to gravity. I believe the reason why we were off and made values have some uncertainty is because when the object fell, we did not take into account friction of the tape on the object and air resistance that acts against the object as it falls.
The percent difference we got is 2.04 %. This value represents how far away we were from the accepted value.
The second column values are the values that our classmate had gotten for their experimental value for gravity in cm/s^2. Afterwards we got the mean of those experimental values by adding all 10 values and dividing by 10, which is located in the 5th column, We were able to get the deviation value by subtracting the mean of gravity value from the experimental values found at each table. We were able to get the deviation^2 value by squaring all the deviation values we found previously. We go the average deviation^2 by taking the average of all deviation ^2 values. We got the standard deviation value by taking the standard deviation of the deviation values on our spreadsheet.
Questions/ Analysis
1. The patterns I found in our value of g is that they were all relatively close to 960 cm/s^2 but still far away from the accepted value of 980 cm/s^2.
2.Our average value of g, which is 961.156 cm/s^2 compared to the accepted value of g, is that we are still far away.
3. The pattern we found in the class' values of g is that there are far from the accepted value of g when we look at it by the standard deviation values.
4. The systematic errors are that of air resistance against the object as it fall in free fall and the friction between the free fall object and the tape, when it is marking the tape. Our random error is that when we measured the position of the object, distance, we might have not gotten the exact value for the position and may have rounded.
5. I believe the key point of this lab apart from knowing how to measure a free falling object with the given apparatus, is that to understand how to look derive an acceleration from the velocity vs. time graph and position vs. time graphs. Another point was to know how far (or close) we were from the accepted value for gravity. With this lab, I learned how to apply statistics aspects to it and learn more on how to use Excel spreadsheets for lab.
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