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High Seas Adventure!

Second Challenge

To start our exploration, we will observe a phenomenon of fluid mechanics known as Archimedes’ principle.

For middle school students:

1. Assign the students into groups (or let them pick)
2. The boat must only be made with materials offered in the store (instructors can pick these materials - recommended materials include tape, cardboard, foam, paper/foam cups, paper/foam bowls, and pins)
3. Using the materials provided, design and construct a barge of your own choosing. You may use the scissors to cut the materials and rulers for measurements, but all other materials must be bought. Instructors should record purchases from the HydroCost application for middle schoolers (Link). If that doesn't work, navigate to http://shodor.org/~rohins/portfolio_ and then clicking on the link labelled "HydroCost Boat Applet (Middle School Version)." Make the boat watertight, but be careful to not use excess materials, as this adds weight. The boat can be completely closed or have open chambers, but remember that there needs to be a place to load the marbles.
4. Any time a team buys materials, the purchase should be recorded through the HydroCost application for middle schoolers. Instructors can add or delete materials depending on what is at hand, and pick prices for each material. Since cost is factored into the final score, stress that groups should not spend too much money on their boats. Margin of error is not a factor for middle school students.
5. Once all construction is finished, place a boat into the tank of water.
6. The instructor will place marbles, one at a time, into the cup until the boat sinks.
7. Keep count of the marbles and note how the barge reacts as the instructor places marbles into the boat.
8. Record the marble count once the barge sinks. Each team’s value should be entered into the “Actual Amount” field in the middle school HydroCost application. A score will be calculated based on this value and the amount of money each team spent.

For high school students:

1. Assign the students into groups (or let them pick)
2. The boat must only be made with materials offered in the store (instructors can pick these materials - recommended materials include tape, cardboard, foam, paper/foam cups, paper/foam bowls, and pins)
3. Using the materials provided, design and construct a barge of your own choosing. You may use the scissors to cut the materials and rulers for measurements, but all other materials must be bought. Instructors should record purchases from the HydroCost application for high schoolers (Link). If that doesn't work, navigate to http://shodor.org/~rohins/portfolio_ and then clicking on the link labelled "HydroCost Boat Applet (High School Version)." Make the boat watertight, but be careful to not use excess materials, as this adds weight. The boat can be completely closed or have open chambers, but remember that there needs to be a place to load the marbles.
4. Any time a team buys materials, the purchase should be recorded through the HydroCost application for high schoolers. Instructors can add or delete materials depending on what is at hand, and pick prices for each material. Students have a limited budget to buy materials - it is important to note that cost is factored into final score, so students may not want to reach their maximum budget anyways. Margin of error is a factor for high school students, and will be elaborated in subsequent steps.
5. To find margin of error, teams should first compute the volume of the boat by summing up volumes of individual components.
6. Use the following procedure to find the weight of the structure and calculate its density:
   
   
   1. Measure the water level in the tank.
   2. Place the completed boat in the tank and measure the water level again
   3. Determine how much water was displaced by the boat.
   4. Calculate the mass of the water that was displaced. This will be the weight of the vessel.
   5. Calculate the volume by summing up the volumes of the boat’s individual parts.
   6. Compute the density of the empty boat. Alternatively, the boats can simply be weighed using a scale.
   
   
7. Calculate the amount of weight the boat can hold without sinking:
   
   (Density of loaded boat) < (Density of water)
   (Mass of boat + Mass of load)/Volume of boat < (Mass of water)/Volume of water
   (Mass of load) < (Mass of water – Mass of boat)*Volume of boat/Volume of water


8. Assume, when fully loaded, the boat will displace a volume of water equal to the boat’s volume just before sinking. Therefore:
   
   Mass of load < Mass of water-Mass of boat


9. Since we know that the Density of water is 1, and we know the volume of water displaced with a load just prior to sinking, we can do the following calculations:
   
   Mass of water = Density of water/Volume of water
   Mass of water = 1/Volume of water


10. We can now substitute the values, and find the mass of the load:
    
    Mass of load < Mass of water-Mass of boat
    Mass of Load < Mass Difference
11. Taking into account an 90% safety factor:
    
    Mass of load < 0.9* Mass Difference,
    Where the Mass Difference is the calculated value of Mass of Water – Mass of Boat


12. Report the amount of marbles able to be held with the 90% safety factor. This will be the predicted value. The instructor should enter this value for each team under the “Predicted Amount” field in the HydroCost application. The program will use this value when determining final score.
    
    Mass of Load/Mass of one marble = number of marbles


13. Place the boat in the water.
14. The instructor should add marbles, one by one, into the boat until it sinks. The students can pick where each marble can be placed. Record the amount of marbles held by the boat before it sinks.
15. Remove the boat from the water and the remove the marbles.
16. Enter in each team’s number of marbles held into the “Actual Amount” field on the HydroCost application. The program should automatically generate a score for each team based on the amount of money spent, the margin of error between predicted number of marbles held and actual number of marbles held, and the amount of marbles held in total. The exact formula used can be found on the "Instructions" button at the top right of the HydroCost application page.

After this is finished, both middle school and high school students should discard all wet, used, and/or altered materials (such as a cup with holes in it), make sure the work area is clean and dry, and return all other materials to their proper places.

On to page 8!