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.

EXPAND to view: Equal Arm Scale Instructions

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?

EXPAND to view: 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 cylinder (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.

Calibrating your scales

Materials

• calibrated masses. If you do not have the set of standard masses in the physics kit, you could use coins in good shape. A 1990 or later nickel weighs exactly 5 grams when newly minted. To make smaller masses, consider paper clips. Some medicine tablets are pure substance: 500 mg of pure aspirin makes a good .5 g mass.
• a calibration sheet. Spring scales included in the kit will have calibration scales printed on them. If you make your own, place the sheet 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.

Procedure

1. On a homemade scale, ark the zero-point of the unextended spring or verify that the equal arm balance pointer aligns to your plumb line. On commercial sprints, verify that the unextended spring shows aligns to the scale zero point.
2. Now add a known mass, and mark the point of the extending spring. Do not exceed the rating of a commercial spring; you may overextend the spring so that it will no longer measure accurately.

   The extension of the spring for a short range will be constant per unit mass. On a commerical spring, verify that the mass measurement is correct. If you used a 5-gram mass for the extension, you can divide the distance between the two marks into five parts.

3. On a homemade spring, extend your calibration points to 25grams. On each commercial spring, verify the spring correctly calibrates masses at its first (smallest) scale point, half-way scale point, and next-to-last scale point. For example, if you have a spring rated for 100g marked at 10g intervals, verify that it measures your calibrated masses correctly at 10g, 50g, and 90g.

Data Handling: Derived quantity measurement

1. Now you need to determine the volume of a regular object. Use some other cube-shaped object which has a mass midrange for your scale; for a homemade scale, use a mass of about 25grams (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 in centimeters 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.
2. Alternatively, you can measure the volume of any of the balls included in the physics kit (you will need to know the masses and densities later, anyway!) Measure the diameter of the ball in centimeters and use the volume equation for a sphere to determine the volume of the ball in cubic centimeters.
3. Now weight your mass, using one or more scales. Take at least three different measurements 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 measurements.
4. 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 measurements.

Report

1. Describe your materials, equipment, an procedures 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 25g within 1 gram, 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 repeat 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.

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