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Physics Honors/AP 1 and 2

LAB: Calibrating Equipment

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Physics Lab

Physics Lab: Making and Calibrating Equipment

Goal: To measure the density of an regular solid.

This requires that you measure two properties directly (mass and volume), then compute the density as mass/volume. You will need to obtain or construct an equal-arm balance and a spring scale capable of measuring 1 gram differences.

How you build your scales depend largely on the materials you have available. BE SURE THAT YOUR PARENTS AGREE TO YOUR USE OF ALL MATERIALS! The possibilities suggested should stimulate your imagination: improve on them and don't limit yourself to them.

Materials and Procedure

Equal arm scales work by comparing one mass directly to another. When the scale is "balanced" and not moving, all gravitational forces sum to zero, so the only factor left is the mass itself.

You will need

  1. the arm: a straight length of wood or metal, lightweight and rigid. Possibilities: dowel, yardstick.
  2. a pivot mechanism: this will take the weight of the arm at the center; the arm must move around this point. Possibilities: suspend the arm on a needle/nail passed through a hole at the center and near the top edge of the arm, or set the arm on top of a narrow ridge, such as a needle or razor-blade.
  3. a support for the pivot: this keeps your pivot from moving and puts it high enough that your arm and pans swing freely above the table. Possibilities: a used milk carton of which you can fasten or embed your nail/needle pivot; a Styrofoam cup which you can put on top of a stack of books. Put something heavy in the bottom of the carton or cup to keep it from tipping over.
  4. a calibration weight: this should be something on one arm which you can slide along the arm to make the balance read zero when your pans are empty. It will compensate for irregularities in weight of the arm and pans. Possibilities: a bent paper clip from which you can suspend rubber bands or other small counterweights.
  5. weighing pans: these are lightweight containers fastened to the each end of the arm. In one you will place calibrated weights, in the other you will place the object(s) to be weighed. Possibilities: flat lids, suspended from the ends by thread, fishing line or wire; paper cones or cups tacked to the ends of the arms.
  6. pointer: this extends at right angles from the pivot point. When it is vertical, your pans are balanced. It needs to be lightweight and rigid. Possibilities: coffee stirring straw, small wooden skewer, fastened at aright angle to the arm at the pivot point.
  7. calibrated arc: this allows you to measure how far from true vertical your pointer is. You will need to place the arc (which should describe part of the circle made by the pointer when the scale is oscillating on its pivot) behind the pointer. How can you center the arc properly?
  8. weights: These are calibrated masses which you will use to counter the mass of the objects you measure. You will need to find or make masses to measure .1, 1 and 5 grams. Possibilties: a 1990 or later nickel weighs 5 grams when newly minted. How can you make a set of 1 gram standards? Some medicine tablets are pure substance: 500 mg of pure aspirin makes a good .5 g mass.
Equal arm balance

Making a spring scale

Spring scales work because the spring extends a specific distance under a specific force. A mass in a gravitational field has weight and pulls the spring.

You will need

  1. a spring which will extend for the range of mass you want to use. You may need to find several springs for different mass ranges. The ones in your retractable ballpoint pen is a candidate for small masses of a few grams. Bend one end of the spring so that it is perpendicular to the rest of the spring and can serve as a loop to hang the spring.
  2. a support from which you can suspend your spring and have room for an object to extend the spring. Possibilities: a nail in a vertical support, dowel extending from a bookshelf, a clear cylindar (like a sodapop bottle; cut the bottom off and take off all the labeling) within which the spring will fit. If you are very clever, you might be able to make the support for your equal-arm balance do double duty.
  3. a thread or lightweight string tied to the bottom end of the spring, to which you can fasten the objects to be weighed.
  4. weights, as above.
  5. a calibration sheet. This needs to be behind the spring so that you can read the distance the spring extends easily. Position the paper so on the support so that it cannot move relative to the spring. Mark the zero-point of the unextended spring. Now add a known mass, and mark the point of the extending spring. The extension of the spring for a short range will be constant per unit mass. If you used a 5-gram mass for the extension, you can divide the distance between the two marks into five parts. Extend your calibration points up to 25 grams.
Spring Scale

Data Handling: Derived quantity measurement

Now you need to determine the volume of a regular object. Use some other cube-shaped object which has a mass about that of 5 nickels. If you don't have a good candiate, choose some medium (I like using firm potatoes) and cut a cube 3 cm per side (if exact, your total volume will be 27 cm3). Measure the sides and estimate the error in each of your measurements--remember that these may be due to irregularities in the cube as well as in your measurements. Calculate the volume of your cube and the possible error in volume.

Now weight the cube, using one or both scales. Take at least three different measurments of the mass (remove and return the mass to the scale). If possible, have someone else perform a mass measurement. Determine the average mass measurement (sum all the masses measured and divide by the number of times you performed the measurement). Estimate the error in your mass measurments.

Calculate the density (mass/volume) of your cube, using your average measurements and your extreme measurement possibilities (greatest amount of error more and less). Determine the error as a percentage of the average density derived from the separate measurments.


  1. Describe your materials, equipment, an dprocedures in sufficient detail that your fellow students could repeat your experiment.
  2. Report your data. Be sure to indicate the amount of error in your measurements. For example, if you can only measure a mass of 25 gms within 1 grm, your error would be 25 ± 1, or 1/25 = 4%.
  3. Present your data in an organized form, preferably in a table, in such a way it is easy to compare results as you repeate trials or vary a specific contributing factor.
  4. Show a sample calculation, if you have calculated values.
  5. If you did a series of experiments, varying something by increasing or decreasing a factor, try to plot your data (y-axis) as a function of the factor (x-axis).
  6. You may use a spreadsheet to calculate your information and create your table.
  7. Summarize your results.
  8. Draw conclusions about what is happening.
  9. Suggest at least one way to improve your experiment.

Follow the instructions at the Moodle to post your lab reports in the appropriate assignment location. Note that AP option students post some labs on the AP options page!