Why does my experimental value of g differ greatly?

[jfnn]

Homework Statement

Hi,

I did an experiment where I launched a soccer ball into projectile motion with my hand and took a video the situation. I uploaded it into the Tracker software to analyze it. The tracker software gave me a x-t graph, a y-t graph, and a y-x graph. From the y-t graph, which was parabolic, I got an equation for the line.

The equation of the line was of the form At^2 + Bt + C = y

I know A, B, and C.

I was asked to find the acceleration due to gravity by observing this equation.

Homework Equations

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Above..

The Attempt at a Solution

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I said that At^2 = 1/2ayt^2

I got this quadratic relationship from a kinematic equation.

I then solved for ay, which is 2A=ay..

I plus my value of A into the equation and get..

-10.752 = ay..

This is obviously higher than -g, which is -9.8m/s^2

(I did it this way in a previous lab and got it correct so I know the logic is right, just not sure why it is above the normal value so much?)

What sources of error would cause this difference in acceleration? I launched the projectile outside on my deck, video taped it, and uploaded into a software for analyzing. Obvisouly, the software asks me to pick the center of mass after every frame, so that is one source of error. Also air resistance is another? But what forces or any error would make the g b higher than its normal value?

Thank you so much,
J

 

[Dr. Courtney]

Tracker is sensitive to what you are using as the length scale in the video and also to various optical effects that crop up with cheap camera lenses.

It is critical for accuracy that all the motion occur the same distance from the camera (in a plane perpendicular to the line of sight) AND that the object being used for the length scale be of a known length and also be in that same plane. If those issues are attended to with due care, and you have a decent camera lens, then the uncertainty in your length determinations will be on the order of one pixel (converted to length units). With sufficient resolution, this can be as small as 1% or better. With sufficient contrast between the object and background, the automated tracking can be very good. If you have poor contrast or automated tracking has trouble following the center of your object, manual tracking on the leading edge will be more accurate.

If you get all these details right, then most of the error in g will be due to air resistance - g will be smaller than expected when you fit position vs. time to a quadratic. Taking due care to make air resistance truly negligible (we use a lead sphere) can yield errors in g less than 1%.

Post your raw data (x and y vs. t) and I can have a look and likely advise you more definitively what may be happening.