[Lab Index]

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

Purpose:

To measure the acceleration of free fall, "g", using an inclined plane.

Discussion:

Around 1600, the amazing Galileo Galilei was able to show, experimentally, not only that the acceleration of objects in free fall was constant, but was able to determine a pretty good value for this acceleration. Galileo performed this feat by rolling wooden balls down long inclined planes, and he didn't even have the luxury of a clock!

Today, we can recreate Galileo's triumph with very little effort using an air track or dynamics track and a motion sensor with a computer interface.

Using the motion sensor and computer software, the computer can plot a real-time graph of velocity vs. time for the motion. The acceleration of the cart is, of course, the slope of this graph. The computer can calculate this for you in an instant, too. Using the computer, it only takes a few seconds to get the acceleration of the cart down the incline. This means that it will be easy to collect accelerations for a wide range of ramp angles - but how do you convert this data into an estimate of "g"?

If a is the cart's acceleration down the track, and is the angle that the ramp makes with the horizontal (see the diagram above), then from the diagram:

so ** a graph of a vs. h should be a straight line with slope
g/L**.

This isn't the way Galileo did it, but it's pretty slick!

Equipment:

Pasco |
motion sensor |

meter stick/metric ruler |
air track or dynamics track |

vernier caliper |
blocks, notebooks, etc. to prop up the incline |

carpenter's level |
ring stand & clamp (optional) |

Setup:

- Start by leveling the incline. Depending on how you set it up, you might want to measure and record the height of what will be the upper end of the track. When you raise the end, you can measure the height from the same location, then subtract to find h. Alternatively, you can use a vernier caliper to measure the thickness of the block, etc., that you use to prop up the track.
- Be sure that you place the motion detector on the
**upper end**of the incline (see the diagram above). - Set up the motion detector to display a graph () of velocity vs. time. You can use the statistics capability () of the software to calculate the slope of this graph, which, of course, is the acceleration of the cart.
- Open the sampling options () dialog, and set the detector to stop automatically after 2 seconds or so.
- Let the cart start down the incline, then start () the detector.
- Remember that you can restrict the statistical analysis to the "good part" of the graph.
- If you can't get decent data, you'll need to make some motion detector adjustments.
- When you are ready to take acceleration data, open
*Graphical Analysis*^{TM}and type your acceleration and height data directly into its data table. Construct a graph of acceleration vs. height. - Be sure to take at least a few trials at each height so you can get a good idea of the uncertainty in the acceleration calculation.

Results:

If you have made several runs at each height, it might not be necessary to add error bars to the graph. Draw the best fit regression line, and get regression statistics for the acceleration vs. height graph, assuming it looks linear. You can calculate "g" from 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"?
- 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