[Lab Index]

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

Purpose:

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

Discussion:

The kinematics of constant acceleration tells us that:

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

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

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!

Equipment:

Pasco Science Workshop |
free-fall Adapter |

meter stick/metric tape |
metal sphere |

ring stand |
ring stand clamp |

C-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.

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

bighelp.

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.

*Science Workshop*^{TM}interface.- Set up the free fall adapter () to measure the time of fall for the sphere.
- Enable keyboard entry () for the height of fall.
- Although the
*Science Workshop*^{TM}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. - Create a data table () to display time of fall, height, and acceleration.
- Create a
graph ()
to display time of fall vs.
height.
- Open the Graph Setup dialog (), and uncheck "Connect Points". You can also enable point protectors if you wish.

- Resize and arrange the windows for a convenient display.

Procedure:

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 Workshop*^{TM} graph window will
only display three data runs at once, but you can transfer the
averaged data to *Graphical Analysis*^{TM} for analysis.
Here's how:

- Line up the free-fall adapter so that the sphere hits the floor switch when it is released.
- Measure the height. Be thinking about the uncertainty of this measurement.
- Click the Record icon () in the Experiment Setup WIndow.
- Put the sphere back in the adapter, and "let fly".
- 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.
- 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>.
- When you have enough data (Ha!), click on "Stop Sampling". Change the height, and go back to step 1.
- Continue until you have taken data for several heights over as wide a range as practical.

Results:

Have
the *Science Workshop*^{TM} program calculate
statistics ()
for the time of fall for each run. Open the *Graphical
Analysis*^{TM} program, and transfer the mean time of fall
and the height for each run to the *Graphical Anslysis*^{TM
}data table. Add
a column to the data table and place the formula
for t^{2} ("=t^2" or "=t*t") in it.

Construct a graph of t^{2} 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 Workshop*^{TM} 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)?

Conclusions:

So, what do you think? In particular,

- How does your value of "g" compare to an "accepted value"?
- Why is it that the slope of a t
^{2}vs. h graph yielded a value of "g"? - What was the measurement that contributed the most uncertainty to your results? How could this be improved if you were to do this experiment again?

[Lab Index] BHS -> Staff -> Mr. Stanbrough -> AP Physics-> Kinematics-> this page

last update July 17, 2000 by JL Stanbrough