Is My Calculation for Free Fall Acceleration Using a Single Photogate Accurate?

[Greenarrow]

Homework Statement

Can free fall acceleration be determined by dropping a marble through a single photogate?
The CPO timer attached to the photogate can measure the time it takes for the marble to pass between the arms. Knowing the diameter of the marble enables one to calculate the speed. If the marble is dropped just above the IR beam, the initial velocity can be assumed to be zero. Therefore, the dropping distance is the diameter of the marble. However, my calculations are showing a ridiculously large value for g. What am I doing wrong?

Homework Equations

Δy = ½aΔt²

The Attempt at a Solution

1) I looked up information on how to determine g using photogate. All information points to using two photogates or a picket fence.
2) The diameter of the marble is 1.9 cm and the time taken by the marble to cross the IR beam is 0.0457 seconds. Since the marble is dropped just above the beam, v_i =0.
Using the equation; Δy = ½aΔt²,
a = 2*Δy/Δt² = 2*0.019/0.0457² = 18.19 m/s²

The logic and reason makes complete sense to me, but the numbers are not what I am expecting. What am I doing wrong?

Thanks in advance.

 

[mfb]

The time is too short. The calculation is very sensitive to the "just above the beam" part - drop it 2 millimeters too high and you get the 0.0457 seconds instead of the expected 0.0654.
The photogate has some finite height as well. It is hard to model this, but you can add free parameters that get adjusted based on experiments.

 

[haruspex]

How exactly is the marble released?

 

[Greenarrow]

I hold the marble so that the light on the photogate turns red (indicating an obstruction), then gradually raise it till it is green (ubobstructed). I realize that this is a very crude method, but I try several times to find the point where the marble is just clearing off from the path of the light beam. Like what mfb replied above, it might be the small difference between the "true" zero initial velocity and what the actual experiment has that makes the difference. I also repeated the experiment with two photogates connected to a CPO timer. This arrangement is capable of measuring the time difference between what is recorded by these two photogates. Still the error is very high. However, when I increase the distance between the photogates, the error is reducing. Now I am suspecting the sensitivity of the photogates. The timer shows a 4 decimal reading though.

 

[CWatters]

The height of the beam window sounds like a good bet. Perhaps try lowering the marble slowly to measure the distance the marble is actually being timed over. Add a pin hole screen?

 

[haruspex]

The height of the beam window sounds like a good bet. Perhaps try lowering the marble slowly to measure the distance the marble is actually being timed over. Add a pin hole screen?

Yes, that seems the most likely. Also, perhaps the line of descent of the marble is not quite central, so it is not measuring the full diameter.