Measurement of g with a free falling plummet

[bravehart]

1. I recently had a lab on free falling and have all the data and percentage amounts from the data sheet, and Position vs. Time.


I'm having a problem creating the slope for the velocity vs. Time. Do I use two different points or just one point?


I used to different tangent lines for the Position vs. time and came up really close to 9.81m/s2.

 

[LowlyPion]

1. I recently had a lab on free falling and have all the data and percentage amounts from the data sheet, and Position vs. Time.

I'm having a problem creating the slope for the velocity vs. Time. Do I use two different points or just one point?

I used to different tangent lines for the Position vs. time and came up really close to 9.81m/s2.

Welcome to PF.

The velocity of course changes with time. If you have your position v. time table then you should be able to derive a table that represents a velocity v. time table. Since g is what you are seeking to measure and it is supposed to be uniform then you would want to verify that it would be uniform through out the table and be prepared to characterize any variances you find that suggest in one part if the table the rate might be different than in other parts. If you observe that there is a minor variation throughout the measurements then you might want to express an error uncertainty in the derived result to convey how accurate your data result may be taking into account your measurement error.

 

[bravehart]

Welcome to PF.

The velocity of course changes with time. If you have your position v. time table then you should be able to derive a table that represents a velocity v. time table. Since g is what you are seeking to measure and it is supposed to be uniform then you would want to verify that it would be uniform through out the table and be prepared to characterize any variances you find that suggest in one part if the table the rate might be different than in other parts. If you observe that there is a minor variation throughout the measurements then you might want to express an error uncertainty in the derived result to convey how accurate your data result may be taking into account your measurement error.

Thank you very much for getting back to me so quickly. Although my Position vs. Time graph has a nice parabolic curve, my velocity vs. Time graph still has a rise in acceleration but, is slightly jagged. Do you think maybe I should use a tangent line in two different spots?

 

[LowlyPion]

Thank you very much for getting back to me so quickly. Although my Position vs. Time graph has a nice parabolic curve, my velocity vs. Time graph still has a rise in acceleration but, is slightly jagged. Do you think maybe I should use a tangent line in two different spots?

You might want to plot the acceleration as a function of time. If it offers more of a staircase effect, then you can consider just using an average of the changes in velocity and express the error bound to each side of the average you find - the maximum slope you might reasonably observe through the data and the minimum slope.
You might then get a result that looks more of the form 9.7±.3 m/s² as a for instance, depending on what you find for slopes.

 

[bravehart]

You might want to plot the acceleration as a function of time. If it offers more of a staircase effect, then you can consider just using an average of the changes in velocity and express the error bound to each side of the average you find - the maximum slope you might reasonably observe through the data and the minimum slope.
You might then get a result that looks more of the form 9.7±.3 m/s² as a for instance, depending on what you find for slopes.

Thank you! My professor had said it could be within 10% maximum for the margin of error, so I will do that!

Thank you so much

bravehart