Physics Lab

Measuring "g" - Time of Fall Method

(uses a Pasco Interface)

[Lab Index]

BHS -> Staff -> Mr. Stanbrough -> AP Physics-> Kinematics-> this page


To measure the acceleration of free fall, "g".


Free fall adapter lab setupThe kinematics of constant acceleration tells us that:

x = v vsub o t plus 1/2 a t squared

so, as long as air resistance is not a factor, if you drop an object from rest from a relatively height, h:

h = q/2 g t squared

where t is the time that it takes to fall the distance h. Solving for g gives:

g = (2h)/(t^2)

Therefore, it is theoretically straightforward to determine the acceleration of free fall simply by dropping something and measuring the time it takes to hit the ground.

Experimentally, however, it is exceedingly difficult to get precise-enough times for meaningful results. (It often turns out that the theoretically straightforward approach is exceedingly impractical in the "real world"...) Over short distances (and short times), human reaction time destroys the precision of the measurement, and over long distances, air resistance becomes a factor so that the acceleration of the object is no longer constant and the calculation is invalid. These considerations (among others) are what forced Galileo to develop his famous inclined plane experiment.

The Pasco Free-Fall Adapter gives us the technology to obtain precision timing for objects dropped relatively short distances, however. When the ball is dropped, it activates a switch to start a very accurate timer. When the ball strikes the pad at the end of its fall, it trips another switch to stop the timer. Simple and straightforward!


Pasco Science WorkshopTM interface

free-fall Adapter

meter stick/metric tape

metal sphere

ring stand

ring stand clamp


Setting Up:

Set up the apparatus as shown in the diagram above. The C-clamp just needs to be tight enough to keep the apparatus from being knocked off the lab table - demonstrate you monstrous strength elsewhere, please.


Setting Up the Pasco Interface:


Turn on "Show Balloons" in the Help Menu. It will explain the purpose of the various icons in the Pasco interface - which is a big help.

  1. Here is what the Calculator Window might look like for a calculation of acceleration. You should understand how this formula relates to the equation shown above.

    experiment calculator window for acceleration
    Hook up and initialize the Pasco Science WorkshopTM interface.
  2. Set up the free fall adapter (Digital plug icon) to measure the time of fall for the sphere.
  3. Enable keyboard entry (Sampling options icon) for the height of fall.
  4. Although the Science WorkshopTM supplies an automatic calculation of acceleration (and I'm sure that it's very nice of them to do so) we are not going to use it. (No "magic boxes, remember?) It is convenient to have acceleration calculated for each trial, however, in order to tell if everything is working reasonably, so you can make your own calculation for acceleration.
  5. Create a data table (table icon) to display time of fall, height, and acceleration.
  6. Create a graph (Graph icon) to display time of fall vs. height.
    1. Open the Graph Setup dialog (Graph Setup Icon), and uncheck "Connect Points". You can also enable point protectors if you wish.
  7. Resize and arrange the windows for a convenient display.


I'm not sure what the Pasco people have in mind for this lab, but the following procedure seems to work pretty well. Of course, if you have a better idea, try it! Basically, each "run" consists of several trials at the same height. I've found that adjusting the height during a run leads to problems (like the ball missing the floor switch...). This also allows you to get a good idea of the timing precision. A Science WorkshopTM graph window will only display three data runs at once, but you can transfer the averaged data to Graphical AnalysisTM for analysis. Here's how:

  1. Line up the free-fall adapter so that the sphere hits the floor switch when it is released.
  2. Measure the height. Be thinking about the uncertainty of this measurement.
  3. keyboard sampling windowClick the Record icon (record icon) in the Experiment Setup WIndow.
  4. Put the sphere back in the adapter, and "let fly".
  5. Record the height of fall in the Keyboard Sampling window, and click <Enter>. Check the acceleration calculation in the data table. If it is unreasonable, find what is wrong, and fix it.
  6. Repeat steps 4 and 5 several times for this height. Once the software gets the idea that you will be keeping the same height, you won't have to retype it - just press <Enter>.
  7. When you have enough data (Ha!), click on "Stop Sampling". Change the height, and go back to step 1.
  8. Continue until you have taken data for several heights over as wide a range as practical.


Graphical AnalysisTM table headingsHave the Science WorkshopTM program calculate statistics (statistics icon) for the time of fall for each run. Open the Graphical AnalysisTM program, and transfer the mean time of fall and the height for each run to the Graphical AnslysisTM data table. Add a column to the data table and place the formula for t2 ("=t^2" or "=t*t") in it.

Construct a graph of t2 vs. height. Add error bars to the graph. (You can get a pretty good idea of the uncertainty of the time of fall from examining the original data and the data statistics in the Science WorkshopTM data table.) Draw the best fit regression line, and get regression statistics for the line. You can calculate "g" fronm the slope of this line, right? Also, be sure to determine the uncertainty in your value of "g". What is the percent of difference between your calculated value and an "accepted value" of "g" (consult the Handbook of Physics & Chemistry)?


So, what do you think? In particular,

[Lab Index]
BHS -> Staff -> Mr. Stanbrough -> AP Physics-> Kinematics-> this page
last update July 17, 2000 by JL Stanbrough