Open source physics photogate kit

Freefall - calculating g

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Freefall - calculating g

Equation for calculating acceleration due to gravity is:

\[g = \frac{v \mathrm{2} - v \mathrm{1}}{\mathrm{\Delta t}}\]

where \(g\) is the acceleration due to gravity, \(v1\) is the velocity in gate 1, \(v2\) is the velocity in gate 2 and \(\Delta t\) is the time between gates.

1) Setting up the photogates

On a single support stand [1], place the two photogates a distance apart. Make sure that the top (first) photogate is connected to the Photogate 1 position on the Arduino Shield.


2) Software

Set-up the software as described in the previous section Using the photogate software.

3) Sample data

In the example shown below, we used a 0.5” wide metal block (12.7mm). Hold the object slightly above the first photogate and release to drop it between the two gates. Save data for analysis.


4) Data analysis

  • From time in gates, calculate velocity, \(v\), of falling object:

    • \(v\) = object length (m) / time in gate (s)
    • \(v1\) = 0.0127/0.00940 = 1.351 \(\mathrm{m}/\mathrm{s}\)
    • \(v2\) = 0.0127/0.00406 = 3.128 \(\mathrm{m}/\mathrm{s}\)
  • From equation, g is given by:

\[g \approx \frac{3.128-1.351}{0.17982} \approx 9.88 \mathrm{m}/\mathrm{s}\]


[1]Additional equipment from Carolina Biologicals. Support Stand $15.50, Part # 707146 and Clamp Holder, $9.90, Part # 707310

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