BHS -> Staff -> Mr. Stanbrough -> AP Physics-> Kinematics-> this page
To measure the acceleration of free fall, "g", using an inclined plane.
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!
Pasco DataStudioTM interface |
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) |
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)?
So, what do you think? In particular,