# Dynamics Experiment A Method for Measuring Mass

## Purpose:

To use an inertial balance to measure mass. First, you will "calibrate" the balance using known masses, then use the balance to find the mass of "unknown" objects.

## Discussion:

"Mass: The quantity of matter in a body. More specifically, it is a measure of the inertia or "laziness" that a body exhibits in response to any effort made to start it, stop it, or change in any way its state of motion."

(Hewitt, Paul, Conceptual Physics, Second Edition, 1992, p. 32)

Scientists measure things. A scientific question to ask is "This definition of mass is very nice, but what does it say about measuring mass?" There are several ways to measure mass - a triple-beam (or electronic) balance measures mass, for instance. The triple-beam balance has a couple of disadvantages, however. First, it is difficult to see how the measurement you make on a balance correlates to the definition of mass given above, and the triple-beam balance won't work where there is no gravity.

If mass measures the "laziness" of an object in response to efforts made to change its velocity, it makes sense that you should be able to measure mass by making an effort to change the velocity of an object and recording its "laziness". This is what an inertial balance does. Two strips of spring steel apply a constant amount of "effort" in order to vibrate a pan back and forth. (A vibration involves speeding up, slowing down, and changing direction (all 3 ways to accelerate), so the state of motion of the object is certainly changed.) If the object can be vibrated back and forth easily, it is not "lazy" - in other words, it does not have much mass. Objects that vibrate slowly have a large mass.

By measuring how fast known masses vibrate on the inertial balance, you can construct a graph that "calibrates" the balance - that is, if you know how quickly an unknown mass vibrates you can use the graph to determine its mass.

## Equipment:

 inertial balance stopwatch C-clamp graph paper masking tape set of standard masses

## Procedure:

NOTE: You will work with one or more lab partners in this lab. You are responsible to turn in INDIVIDUAL lab reports, however. Your lab report should include a data table, your graph, results for the "unknowns", and analysis.

### Part 1 - Calibrating the Balance

The instructor will demonstrate how to set up the inertial balance. Be sure to clamp one end of the balance to the table so that the other end can vibrate freely in the air beside the table. Contrary to what the picture shows, it is probably easier to clamp the balance under the edge of the table instead of on top of it. When you place objects in the balance pan, you will need to use small pieces of masking tape to keep them from sliding about in the pan.

The object of calibrating the inertial balance is to come up with a graph that shows the response of the balance when a range of masses is placed in it. To do this, you will need to do some careful planning. Here are some hints and pointers:

• You will need to use as wide a range of masses as practical - from 0 grams up to as much mass as the inertial balance will hold without buckling. Most of the balances we have will hold 500 - 600 grams. I recommend changing the mass by about 50 grams per trial. The "heavy duty" models will hold more, and you might want to increase mass by 100 grams or so per trial. Don't worry, you won't get too much data...You don't have to take the masses in strict order - you can come back and fill in "gaps" in your data.

• It might be wise to time each mass more than once to catch timing or counting mistakes.

• You can determine the response of the inertial balance by measuring its period - the time it takes for one complete vibration (over and back), or by measuring its frequency - the number of vibrations of the balance pan in a unit of time (per second, say). Either period or frequency will produce a usable graph (although the graphs will be differently shaped) - it just depends on which measurement you find most convenient. Actually, you don't need the period or frequency itself - the time for 30-50 vibrations (30-50 periods) or the number of vibrations in 30 seconds is easier to work with...

• Don't try to time one period, or determine the number of vibrations in one second! Record the time for 30 to 50 (or so) vibrations, or the number of vibrations in 30 to50 (or so) seconds.

• Construct a data table to record your data. Some sample data tables are shown below. Which data table you use depends on whether you are working with the period or the frequency of the inertial balance.

### Part 2 - Measuring "Unknown" Masses

You need to demonstrate that you can measure the mass of an object using the inertial balance. Your instructor will place several objects of "unknown mass" where you have access to them. Determine the mass of 2 of them using your inertial balance. Some hints:

• You can "run" the unknown masses on the inertial balance before you draw your graph, but you determine the mass of the unknown from your graph. For instance, in the graph shown at the left, the unknown mass had 18 vibrations in 20 seconds. From the graph, its mass is 250 grams.

• Be sure to record your measurements for the unknown masses in a data table (the same one will work) and be sure to identify each unknown.

• You can also measure the mass of the unknown in a more conventional manner - using a triple-beam or electronic balance, for instance. This would provide a check on the accuracy of the inertial balance.

## Results:

Draw a graph of (known) mass versus the response measure (period, frequency, 50 periods, whatever) you have chosen. Use graph paper, and draw the best smooth curve through your data points. Use your graph to determine the masses of your unknowns. Some sample graphs are shown below.

## Analysis:

1. What are some advantages of timing 30-50 (or so) vibrations of the inertial balance instead of just one?
2. How accurately does the inertial balance measure the masses of your unknowns? What limits its accuracy? (Be specific, and support your answer.)
3. Would the inertial balance successfully measure mass in the Space Shuttle when it is in orbit around the Earth? Why do you think so? What about a triple-beam balance, which is the more-common way of measuring mass on Earth?

## Going Further:

Astronauts making extended space flights tend to lose muscle and bone mass due to the "zero-g" conditions in space. This means that it is critical to monitor an astronaut's weight or mass during their stay in space - but the astronaut is "weightless"! If you are interested in space flight or space medicine (or physics!?), you can research how this is done.

adapted from Haber-Schaim, et. al., Laboratory Guide for PSSC Physics, Fourth Edition, D.C.Heath and Company

last update November 23, 2007 by JL Stanbrough