L21.  Archimedes' Buoyancy Challenges

About submitting your work: A wiki will be created for this lab. Write your report in your wiki. If you have a partner, you'll write a group report. After the due date, you'll be able to see how other students solved these problems.

Goal:  To use Archimedes' Principle in the measurement of density

Prelab: Before doing this lab, submit your solutions to these problems. Your solutions to some of the problems can guide your methods below.

Equipment: You should have assembled these items of equipment in advance of the lab.

Experimental design:  Here are some constraints and considerations in your experimental design:

  • You may have noticed that an item missing from the list of equipment (and one that you may not use) is a traditional pan balance for measuring mass. For massing, design methods that use fluid principles, unless stated otherwise.
  • You have a variety of methods for measuring volumes. Two of them were described in the prelab problems. For objects that have geometric symmetry such as cubes, spheres, and cylinders, you may determine the volume by making measurements of dimensions and using them in the appropriate volume formula.
  • Any design must have both a theoretical and experimental component. The experimental part is what you do with the equipment and what measurements you make. The theoretical part provides the explanation of how and why the experiment achieves the goal.
  • You may assume the value of 1000 kg/m3 for the density of water. For all other materials that you use, assume that the density is unknown until you measure it.

Working with a partner: You may work in groups of 2 students. Students who work in groups will do all work together, including writing the wiki report. In order to work with another student, however, both students must have submitted the prelab problems beforehand.

If you work with a partner, email me the names of the partners and the last name of a famous scientist. Avoid names that everyone tends to think of first like Einstein and Newton. The name of the scientist you pick will be the pen name under which you write your wiki report. I'll create a wiki with that pen name and both partners will have editing privileges in the wiki. I'll expect to see evidence in the wiki log that both partners participated in writing the wiki report. One thing to watch out for, though, is that two people can't edit simultaneously. So plan your editing. Also, make sure you don't delete something your partner wrote that he/she wouldn't want to have deleted.

If you work alone, just email me the name of a scientist. That will become the pen name for your wiki report.

When you write your reports, don't use your real names. Use only your pen name.

Part A. Massing with Archimedes

We'll give detailed instructions for this part. You'll be on your own for Part B for the most part.

The specific goal of this part is to determine the density of a solid object (the metal cube, cylinder, or sphere with a hook) that sinks in water.

  1. Review the second problem of the prelab problems, since the method described there is the one you'll use here.
  2. Determine the reading of the spring scale with the object in air and with the object completely submerged.
  3. If the object is regular in shape, measure the relevant dimensions of the object to use in calculating the object's volume. If the object is irregular in shape, devise a water displacement method to determine the volume.
  4. Calculate the mass of the object two ways:
  1. Use mg and the value of the scale reading in air.
  2. Use both values of the scale reading (in air and in water) together with Archimedes' Principle and Newton's Second Law.
  1. Calculate the density of the object using the volume and the mass from 4a and also using the mass from 4b. This will give you two values of density. Which do you expect to be more accurate?

Part B. Density of a penny

The specific goal of this part is to determine the mass and density of a penny. Rather than giving you a step-by-step method, we give only these constraints and considerations.

  • You aren't allowed to use a spring scale for this challenge.
  • Find a way to improve the accuracy of your measurements by using many pennies.
  • Pennies have changed composition over the years. An internet search can help you to sort pennies by date in order to use pennies that have the same composition.

Writing your report

Include all the usual parts of a lab report according to the Guide to Writing Lab Reports.  In addition to the starred components, include the following:

  • Theory for each part: It's important to provide theoretical justifications for your methods. Your solutions to the L21 prelab problems should be helpful here.
  • List of apparatus
  • Method:  Describe your method of Part B completely and clearly. Otherwise, the teacher will not know what you did. Use diagrams as needed to make your method clear. You do not need to describe your Method for Part A unless you deviated from the given instructions.
  • Legend of symbols: Define all symbols that don't have obvious meanings.
  • Calculations: Show complete calculations of the densities of the objects in Parts A and B.