Dynamics Experiment
A Method for Measuring Mass



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.


"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.

[Image of an Inertial Balance]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.


inertial balance



graph paper

masking tape

set of standard masses


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:

[Image of Sample Data Tables]

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: How to find the unknown's mass


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.

[Image of Sample Graphs]


  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