Objectives: By making a penny barge from limited materials, students will learn to calculate surface area and volume, and witness buoyancy and Archimedes Principle in action as they attempt to sink the barge/container.
Assignment/Design Brief: Design and construct a floating cardboard container with 144 square inches or less of surface area to hold as many pennies as possible before capsizing or sinking. Coat container with one layer of masking tape on the exterior to help with water resistance.
* Container must support pennies as load for testing.
* Container calculations must be completed at the start of class to be considered for competition.
* Container must have an open top to load the pennies.
* Container must float freely well above the bottom of the tank to be tested.
* Container may only be constructed of cardboard, and masking tape with tape for joints of materials. You may coat the container with one layer of masking tape. More that one layer will disqualify you.
* Total surface area of all cardboard used, including flaps and tabs may not exceed 144 square inches of surface area.
* Container may not be tall enough to rest on the bottom of the test tank.
Testing: Calculate the number of pennies to sink your container. Record this number on the chart provided in class. The Container will be tested in test tank provided in class. Testing will consist of loading your container with half the predicted penny amount and floating your structure to load the rest until the container capsizes or sinks. The rest of the pennies must be counted on the way into the container. Retrieve pennies and dry them off. Record penny number on chart provided in class.
* Structures not ready (not constructed, pennies not calculated) to test at the beginning of class on the due date will not be ranked and receive no higher than a “C” (80) when tested. This means calculations for pennies must be complete.
* Containers that exceed the 144 square inches of material will not be disqualified and container must be reproduced. Containers that use materials other than cardboard and masking tape will be disqualified and must be reproduced. Disqualified vessels will be tested and ranked in the lower grading bracket starting with an 80 for the container that holds the most.
* Containers may be disassembled for proof of materials after testing is completed.
Teacher Notes: Students can use any type of cardboard but note that thicker cardboard will weigh more and require less pennies to sink. The tank hold enough water to test the tallest container designed by the students. Students must show their calculations to prove that they met the material or surface area criteria of the challenge. Students will calculate the volume of their container and weigh their container to then calculate the number of pennies needed to sink the container. Record the predicted penny amount for each student to reflect on why their container held more or less than predicted.
When testing, have the student testing their container put half the number of pennies in before placing the container in the test tank. With this step, the students can observe that the container is submerged halfway into the water because the container has half the weight needed to sink the container. The students observing can count stacks of ten pennies to help the process go quicker. Multiple tanks can be used to quicken the process as well. Students can also be grouped into teams so that they cheer each other on. The team total could then be ranked.
I hold this competition with up to 21 students per class and grade them according to their rank. Students must submit 3 designs with surface area and volume calculations completed prior to selecting the container they want to build. The designs must be three different shapes so that they note that the volumes will be different even though the surface area is the same.
The number of pre-1982 pennies has a mass of 3.1 grams. However, pennies made after 1982 are about 2.5 grams. So the average is about 2.78 grams.
Water Weight = 62.4 pounds per cubic foot
1 cubic foot = 1728 cubic inches
1 gram = 0.035 ounces
Step 1: Container Design
Provide 3 different design sketches with measurements while adhering to the material limitations. Include the top, front and side views of the container or an isometric view to show the measurements of each design.
Provide surface area calculations to prove that you have not exceeded the allowable surface area. Show all math.
Provide volume calculations for the three different penny barges to determine the largest volume. Show all math.
Step 2: Build the Container
Step 3: Determine Number of Pennies to Sink Container
Calculate the volume of the container in inches and convert to cubic feet by dividing by 1728 cubic inches per cubic foot.
_________ cubic inches / 1728 cubic inches per cubic foot = ___________ cubic feet
Determine the weight of the water that must be displaced by the container by multiplying the amount of cubic feet of the container by 62.4 pounds per cubic foot, the weight of water.
________ cubic feet X 62.4 pounds per cubic foot = __________ pounds.
Convert the water displacement to ounces by multiplying the pounds of water by 16 ounces per pound.
_______ pounds X 16 ounces per pound = __________ ounces
Determine the amount of penny weight needed to sink container by subtracting the weight of the container from the ounces of water displacement.
_______ ounces of water displacement - ________ ounces of container = _________ total ounces of pennies needed to sink container
Convert penny weight to pennies needed to sink the container by dividing the ounces of total pennies by the weight of one penny, .0973 oz.
_______ ounces of pennies / .0973 ounces per penny = _________ pennies
Step 4: Test Container
Count out 1/2 to 3/4 of the pennies needed to sink the container.
Place the pennies in the container prior to placing the container in the test tank.
Notice where the container rests in the tank with the initial penny load. If half the pennies were placed in the container, then the container should be sitting half above and half below the water line.
Step 5: Sink the Container
The actual number and the calculated number should be pretty close if not exact.