Inertial Mass Printer Friendly Version
Purpose

The purpose of this lab is to acquaint the student with the properties of oscillatory motion using an inertial balance, the use of the LabPro motion detector, and data analysis techniques that will show the relationship between the variables for period and mass.

Laboratory set-up

We will be using the following equipment: 1 inertial balance, 4 extended test-tube clamps, 24 washers, 1 C-clamp, and triple beam balances. A LabPro should already be present on the demonstration desk at the front of the room.

We will first use the calibrated triple beam balances to measure the gravitational mass (in grams) of each test-tube clamp to two decimal places. You may number the clamps with pieces of masking tape. Since we are conducting this lab together as a class, we will record our results both on the board and in Data Table #1 in the designated blanks. Do NOT switch clamps! You will then mass each set of 6 washers (in grams) as we incorporate them into the experiment.

 Clamp Description Mass (g)
 test tube clamp #1
 test tube clamp #2
 test tube clamp #3
 test tube clamp #4
 1st set of 6 washers
 2nd set of 6 washers
 3rd set of 6 washers
 4th set of 6 washers
 unknown cylinder w/rubber bands

Purpose

The purpose of this lab is to acquaint the student with the properties of oscillatory motion using an inertial balance, the use of the LabPro motion detector, and data analysis techniques that will show the relationship between the variables for period and mass.

Clamp your inertial balance to the edge of your table so that the pan with the "hole" is free to vibrate. Set up your motion probe on a chair so that it "looks at" the edge of the pan. There should be a minimum of 40 cm between the pan and the motion probe. When the experiment begins you are to ever so slightly displace the balance towards the probe (parallel to the floor). Do NOT force the balance to make large amplitude vibrations - this will make your results less accurate and will DAMAGE the balance.

After your apparatus set-up has been cleared by your instructor, launch LoggerPro 3.1 The program should automatically set up graphs according to the connected sensors. With the motion detector properly connected, the program should display graphs of position versus time and velocity versus time. Place the motion detector so that it can watch one side of the inertial balance. When you are ready to obtain data, hit the "Collect" button on the top right-hand side of the program window.

On your screen you should see the inertial balance's location. Displace the balance slightly left or right and make sure that the detector tracks its entire vibration. If part of the motion disappears from the graph, call your instructor over to help you align your probe. When this test checks out, you may begin to gather the actual data for the experiment.

Note: Remember to not allow the balance to vibrate closer than 0.4 meters to the sensor during collection. This will cause faulty returns and skew the data.

Data Collection

We will record our data for each trial before collecting data for the next trial. Each mass is to be repeated two times. The information required in Data Table #2 can be gathered from your position-time plot by letting your mouse "hover" over the endpoints of each graph's "good section."

Start with an empty balance and then add the requested number of clamp(s) and washers completing two trials with each specified clamp collection. Record the whole number of vibrations and their elapsed time to three decimal places.

 Data Table #2 Trial #1 Trial #2 Clamp Description ElapsedTime NumberVibrations ElapsedTime NumberVibrations
 empty balance
 test tube clamp #1 w/no washers
 test tube clamp #1 w/6 washers
 test tube clamps #1, #2 w/6 washers
 test tube clamps #1, #2 w/12 washers
 test tube clamps #1, #2, #3 w/12 washers
 test tube clamps #1, #2, #3 w/18 washers
 test tube clamps #1, #2, #3, #4 w/18 washers
 test tube clamps #1, #2, #3, #4 w/24 washers
 unknown cylinder with rubber band

When we have finished collecting data, complete Data Table #3 with your lab partner. Remember that the period of each clamp collection reprersents the time in seconds for one complete vibration which is calculated by dividing the total time by the total number of vibrations. Report your answers to three decimal places in the third column.

But what is the difference between the 4th column of values for Period^2 (T2) and the 5th column of values for T2for mass alone? In our experiment each collection of clamps was vibrated in the pan of an inertial balance. If we could have vibrated them without any supporting equipment like "Samantha the witch in the 1960's TV series Bewitched," then we would not have needed column 5. But we, unfortunately, must "remove" the behavior of the inertial balance from each of our trials.

To do this, we must substract the T2 of the empty balance (in column 4) from each T2 entry in column 4 to get the value for the T2 of the mass alone in column 5.

Also notice that the masses requested in this table are to be in kilograms (kg) not grams (g). This means that each mass entry will have five (5) decimal places!

 Data Table #3Clamp Description Trial #1 period (sec) Trial #2 period (sec) averageperiod (sec) Period^2T2 (sec2) T^2for mass alone (sec2) mass in pan (kg)
 empty balance
 test tube clamp #1
 test tube clamp #1 w/6 washers
 test tube clamps #1, #2 w/6 washers
 test tube clamps #1, #2 w/12 washers
 test tube clamps #1, #2, #3 w/12 washers
 test tube clamps #1, #2, #3 w/18 washers
 test tube clamps #1, #2, #3, #4 w/18 washers
 test tube clamps #1, #2, #3, #4 w/24 washers
 unknown cylinder with rubber band

Graphical Analysis

EXCEL will now graph your data from Data Table #3 (with the exception of the first row for the empty balance and the last row for the unknown cylinder). Open the file on your shared drive called InertialMass-1.xlsx. You will most likely be asked to open the file as "read only" - that is fine. As soon as the file is open, use File Save As to rename the file as

InertialMass_LastnameLastname.xlsx

 What is the name of your file?

Now input your final AVERAGE values for Mass and Period2 for mass alone. As you enter your data, your graph has been preprogrammed and will grow. Mass (M), measured in kg to 5 decimal places; will be placed on the x-axis and Period2 (T2), measured in sec2 to 3 decimal places, will be placed on the y-axis. Remember to NOT ENTER the data for the trial using the unknown cylinder. When your graph is finished, be certain that any points that are obviously out-of-line have been rechecked for accuracy - either in measurement, or for a mistake in typing.

Conclusions

 1(a). State the equation of your line being careful to use the correct "variables" - T2 for y and M for x - as well as your actual numerical values for the slope and intercept.

 1(b) Use this equation to interpolate a value for the experimental inertial mass of the unknown cylinder by substituting the value for its average T2 for mass alone from Data Table #3.  Place your work in the area provided below.                 According to your equation, what was the experimental mass of this cylinder?

 1(c). Calculate the percent error between the measured static gravitational mass of the unknown cycliner found Data Table #1 and its experimental inertial value calculated in question 1(a).  Place your work in the area provded below.                 What was your trial's percent error?

 2. What is the significance of the y-axis intercept of your trend line, or regression line, in question 1(a)?