The Fleet Afloat!
A Design Project
Objective: Students will design a concrete barge which will float and carry a maximum cargo. In this experiment the students will be learning to work with the component materials used to make concrete and building and testing a concrete structure for physical properties.
Density is a measure of the compactness of a material. It is a measure of how much matter is squeezed into a given space. Density is the amount of matter per unit of volume.
Whether an object will sink or float in water depends on its density. An object will float if it is less dense than water. An object will sink if it is more dense than water. If an object has a density equal to that of water, it will neither sink nor float. The density of water is 1.00 g/cm3. The apparent density of an object can be changed by either changing the mass of the object, the shape of the object, or both. For a given mass of concrete, the apparent density can be altered by changing the volume it occupies (i.e. volume displaced when placed in water). Concrete can be made to float if it is shaped like a boat. A boat-shaped or hollow object will displace a volume of water greater than the actual volume of solid material in the object. The object is said to be "buoyant" when it floats due to low density. By spreading out the concrete used to make the boat over a larger volume, the apparent density of the boat becomes less than that of water. Hence the boat floats!
Time: 90 min. (1 class period for making the barges and 1 class period for testing)
Materials and Supplies:
The following materials are needed for each group of 2-3 students:
- mold to make barge
- various aggregates
- pea gravel
- small Styrofoam balls
- crushed corn cobs
- 2-3 pairs of gloves for concrete handling
- spreading utensil for spreading concrete in barges
- boat or tray to demonstrate buoyancy with cargo
- 1-2 pounds of washers, weights or lead shot
General Safety Guidelines:
- It is easiest to form the canoe by hand, but cement is caustic. Wear plastic gloves.
- Wash your hands well after use.
Design Competition Parameters:
- The barge or canoe must be constructed from materials (cement and various aggregates) provided by the instructor. The form used to create the barge or canoe is to be provided by the students.
- The proportions of the ingredients used in the cement mixture are to be chosen by the students using the following as a guide, not a recipe:
3 parts aggregate: 2 parts cement : 1 part water
100 grams of cement is sufficient for one Dairy Queen boat.
- Once constructed, the barge or canoe should be cured for at least 24 hours.
Design Testing Procedures:
- The mass of each empty barge or canoe will be measured. The lighter the ship the more points it receives. Any vessel less than 150 grams earns the maximum points value.
- Each barge or canoe will be placed in the water. The empty barge or canoe must float for one minute before the cargo will be added. A cargo will be added in increments until the point when the ship begins to take on water. Each ship must float for 1 minute prior to the addition of each additional cargo increment. For the canoe, whether the canoe leans or floats level will be noted.
- The mass of the cargo will be measured. For every 50 grams the ship holds, it will receive one point.
- A ratio of (mass of cargo):(mass of ship) will be calculated to determine each barge's class rank.
- Barges which fail to float without any cargo will be assigned a predetermined point value.
- Points will be awarded to each barge based on its class rank.
- The cost of construction will be calculated for each boat which successfully floats for 1-2 minutes to determine its class rank. (optional)
- The amount of leakage will be determined and point values will be given for the different levels of leakage.
- Suppose you and a friend are in a canoe with a load of rocks. If you throw half of the rocks overboard, will the water level of the pond go up, down, or stay the same? Make note of your prediction.
- In a container of water, float a boat loaded with a cargo of washers or other uniform weight. Make sure the water's height is greater than the combined height of the washers and the boat.
- Mark the water level on the container and on the side of the boat.
- Put the cargo of washers in the water. Mark the new water levels on the container and the side of the boat.
- What happens to the water level on the side of the boat when the cargo is moved from the boat to the water?
- If you see a boat riding high in the water, which is it more likely to be carrying: lead bricks, glass marbles, or Styrofoam cups?
- What happens to the water level on the side of the container when the cargo is moved from the boat to the water? Was your prediction correct?
- Describe the shape, dimensions, and composition of your barge. Draw an illustration.
- What was the limiting factor in your barge design?
- b. How would you change your barge's design to improve this ratio?
- How could you change the density of your barge/canoe without changing its mass?
Notes for Teacher:
- Several criteria are listed so that the teacher may choose the guidelines upon which to rank the barges/canoes.
- This experiment emphasizes the physical geometry of the barge and therefore may be most suitable for a physics course when discussing principles of density and buoyancy.
- The cargo could be lead shot, washers, weights, or any other material of uniform mass. The one minute waiting period prior to the addition of more cargo may need to be shortened depending on class period length and the number of barges being tested. However, a waiting period is necessary to provide time for water to enter the barge.
- The form materials could be provided or the students could be directed to bring in their own forms, allowing their imaginations to wander. Limits might need to be set in terms of dimension, weight, or amount of concrete/cement available. Possibilities for the barge forms are travel soap dish or a travel toothbrush holder or even an old tennis shoe. Dairy Queen banana split boats, foam insulation, plastic weighing dishes, old butter/margarine containers are suitable for the canoe.
- Foam meat trays or plywood boards make good bases for the barges/canoes to be set on and are very helpful when moving them from the building site to the curing site (if different). The ships should be covered with wet rags or plastic while curing to help retard evaporation and improve hydration.
- A wash tub, 5 gallon bucket, or a small child's swimming pool could be used for the testing waters. Do not use ponds or swimming pools. Cement is caustic to living things. A video recording of the testing could also be made. The video could be set out in the hallway and replayed during parent conferences for the parents to view while waiting to speak with you - great public relations.
- This activity could be tied into a holiday such as Labor Day, Columbus Day or Washington's Birthday observance. Decorations could be added to the barges and a competition held to determine the most aesthetically pleasing barge. The art classes might be asked to judge the barges.
- Note: Pre-assign dollar amounts to quantities of materials in order to calculate the cost of the boat. (optional) This option allows discussion of economy and efficiency.
Answers to Questions:
- Will go down. i.e., boat rides high in the water
- Styrofoam cups
- The level goes down!
Removing the cargo lowers the water level by a volume, V1, equal to the cargo's mass over the apparent density of the boat and cargo. The water volume, V2, raises from the cargo put into the water by its mass over its density.
Simple math yields: V2-V1=-0.57*Cargo Mass
Note that the negative sign means down.
- Answers vary based on students design.
- Possible answers: heavy mass; low surface area; poor construction; setting time inadequate.
- a. Answers vary.
b. Possible answers: change aggregates; change concrete component proportions; different shaped form.
- By changing its volume.