The purpose of this lab is to measure the gravitational acceleration constant *g* by measuring the rate at which a falling object increases its speed. We also learn the use of computerized lab equipment, which is helpful for later experiments too.

If you need the .pdf version of these instructions you can get them here.

In this lab, you will drop a ruler through a photo gate. From this we can infer the rate at which the ruler will accelerate due to the earth’s gravitational force. The clear plastic ruler will be marked at regular intervals with a masking tape that will block the light beam of the photo gate and turn on and off the timer which sends the results to the computer. The times are recorded by the computer and displayed on the monitor. Using the distance between successive pieces of masking tape and these times, the computer will perform the calculation of the average velocity of the ruler in these intervals during its fall. The results can be displayed graphically on the monitor in various instructive ways.

We need to get the interval *d* between two successive leading edges of the tape pieces, i.e. one piece of tape and one blank spot. To be more accurate, measure the distance *D* from the first leading edge to the last one on the ruler and divide it by the number of intervals d between them.

To be more accurate, measure the distance *D* from the first leading edge to the last one on the ruler and divide it by the number of intervals d between them.

As well as measuring *D*, we need to make an estimate in our error for our measurement of *D*. Things you should take into account are the accuracy of your measurement tool, and how straight your masking tape is. Fill in the table on your worksheet with your values for *D,d* and their respective errors.

Now, connect the photo gate output to the interface box by plugging its cable into the top socket (labeled “DIG/SONIC 1”) of the black interface box (“LabPro”). Test the photo gate: block the photogate beam with your finger and see the red light on the cross bar of the photogate turn on.

Get the computer ready for data taking:

- Turn on the computer and check the system by following these instructions: double click the icon “Exp2_xva_t”. A window with a spreadsheet on the left (having “Time, Distance, Velocity, Acceleration” columns) and empty graphs on the right (distance, velocity and acceleration vs time) comes up. On top is a window “Sensor Confirmation”. It should show:

Sensor Specified In File: | Sensor To Set Up: | Where: | Use: |
---|---|---|---|

✔Photogate | Photogate | DIG1 on LabPro | ✔ |

- Click OK

- If you don’t see the above do the following:
- Click Experiment→Set Up Sensors→Show All Interfaces→DIG/SONIC1: you can check the photogate by blocking it and seeing “Unblocked’ go to “Blocked”.
- Click “Close”

- Click Data→User Parameters: the window “User Parameters” comes up. Enter your value for the distance
*d*into the program in the value box.

Name: | Value: | Units: | Places: | Increment: | Editable: |
---|---|---|---|---|---|

PhotogateDistance1 | your value of d | 4 | 1.0000 | ✔ |

- Click OK
- Click Experiment→Start Collection. You should see “Waiting for Data” on the right hand side graph.
- While the message “Waiting for data” is on hold the ruler just right above the photogate (with the first masking tape edge closely above the light beam) and then drop it through the photo gate so that the tape on the ruler interrupts the light path of the photo gate. Make sure that the ruler is aligned vertically before you drop it, so that it is oriented perpendicular to the light beam during its fall. After the ruler has fallen through the photogate you see the collected data on the screen: Time, Distance, Velocity, Acceleration. After a little while the corresponding graphs appear on the right. If you waited too long before dropping the ruler and the “Waiting for Data” message has disappeared restart. Any time you want to repeat your measurement simply restart.

- On the measurement program you should have at least 5 velocity values and a straight line velocity - time graph without a kink on the right. If not repeat the measurement.

- Copy the
*time*and*velocity*values into the table on your worksheet.

- Make sketches of distance vs time, velocity vs time and acceleration vs time in the grids supplied on your worksheet. Label axes, units and scales. Make sure your vertical axes start their scales at zero. If one of the graphs on the screen does not start from zero click on the graph that doesn’t, click Options→Graph Options and choose “Autoscale from 0”.

We are now going to make a plot of *v* vs. *t* to determine the value of *g*. In this plot we need to have estimates for our error in *v*. The error in *v* comes from the error in our measurement of *d*. In the preparation assignment you will need to work out how to relate the error in *v* to the error in *d*. As by the time you are doing the lab you should have done this you should be able to complete the table on your worksheet and then fill in the *y* error box on the plotting tool. We will consider that errors in *t* are too small to worry about (the computer is very accurate, or at least much more accurate than you or I are at measuring a length with a ruler!). This means you do not need to enter anything in to the *x* error box and you should select the option that there are errors only in *y*. Do you think this graph should go through (0,0) (or in other words at *t=0*, should we have *v=0*)?

Go ahead and make your plot of *v* vs. *t*. The slope of the graph should be equal to *g*? How does the value you obtain compare to accepted value of 9.81 m/s^{2}?

In the approach we took above we estimated the error in *g* based upon the propagation of what we expected to be the most significant source of error in our experiment. Another approach we can take is to make several measurements, and we will do this using the built in fitting tool in the measurement program. This tool, unlike the one you just used, will **not** take into account the uncertainty in your input values. We will instead estimate the error in our measurement using the approach we used in Lab 1 (Equation 1.5b) to estimate the error in an average.

You are going to drop the ruler through the photo gate as you have did before. In order to get this value from the computer you click the graph, then click Options→Graph Options and check Velocity, click Done. Then click Analyze→Linear Fit. Read the slope from the popup window with the fit results. Repeat this 5 times and enter your results in the table on your worksheet. Now use equation (1.5) and (1.5b) from Lab 1 to calculate the average value of *g* and the error in the average value of *g*. Compare this to both the accepted value and your previous value. How do the errors you estimate using the two approaches compare to one another? Which one do you think is a better estimate?

In this last part, you will see what happens to the initial (“initial” is the time of the first interception of the photo gate beam) velocity *v _{0}* if the ruler is dropped from higher up above the photo gate.

Hold the ruler a few inches above the photo gate and then drop it through the photo gate. Then look at the computer generated plot of velocity vs. time and record the initial velocity *v _{0}* of the graph on your worksheet. Is your initial velocity greater or less than the one you recorded earlier?

When you have done all the required parts of the experiment make sure that you have filled in your worksheet and thought about all the questions that are asked on this page. Let one of the TAs know that you are ready to discuss the results from lab. Note that they will want to see that you understand the concepts behind what you are doing as well as the actual experiment itself. After discussing with you they may either tell you that you've done a good job, or ask you to do something again if there is a problem. Make sure you don't leave till the TAs have told you it's ok to go!

**Before you leave please make sure that all equipment is left in the way you would hope to find it if you were in the next section!**