11Th Grade Summer Lab

Name: ______Date: ______

11th Grade Summer Lab Due: August 30, 2011

Science and Mathematics Component:

This component will count as a test grade in both Physics and Mathematics. The objectives of this assignment are to assess your ability to conduct an investigation, make the proper inferences, and create an effective science lab report supported by appropriate mathematical explanation. Please feel free to use outside research sources (i.e. internet, library resources) to provide yourself with appropriate background knowledge. You may choose to work alone or in groups of up to four students.

The Assignment: Aluminum Foil Boat Buoyancy Experiment

Part I: Complete the experiment at home. You may work in a group up to four people. For the experiment you shall construct five boats of different surface areas, using the same basic design, and determine how the surface area of the aluminum foil affects the cargo carrying capacity of the boat. NOTE: Try to construct the boats using the least amount of aluminum foil and NO scotch tape.

Part II: Type up a physics lab guided by the rubric provided. You must state the problem, approach, the materials used, the procedures taken, data and graphs explaining results, analysis and conclusion. Please use the enclosed rubric as a guide when creating your lab report. Your report should have seven sections, one for each heading in the rubric.

You MUST hand the lab to Mr. Holloway in Room 300. You may also email your papers before the first day of school to Ms. Goetz at: [email protected] . (There will be a general penalty of one grade reduction per each day late.)

Aluminum Foil Boat Buoyancy Experiment Information:

INTRODUCTION: You know from experience that if you drop a steel bolt in a bucket of water that it will sink like a rock to the bottom. On the other hand, you know that ships made of steel can float. How does it work?

What determines whether an object floats or sinks? It's the density (mass per unit volume) of the object compared to the density of the liquid. If the object is denser than the fluid, it will sink. If the object is less dense than the fluid, it will float. If the object has the same density as the fluid it will neither sink nor float.

With a steel-hulled ship, it is the shape of the ship's hull that matters. The hull encloses a volume of air, so that the total density, defined as:

(mass of steel hull  mass of enclosed air)

volume is less than that of water. Name: ______Date: ______

Archimedes discovered that an object immersed in water displaces a volume of water equal to the volume of the object. The displaced water creates an upward force on the object. If the weight of the displaced water is greater than the weight of the object, the object will float.

In this project you will make some boat hulls of the same shape and different sizes using aluminum foil. Can you predict how many pennies each of your boats will support without sinking?

PROBLEM: How does the volume (length x width x height) of an aluminum foil boat affect its buoyancy (the amount of cargo the boat can carry and still stay afloat)?

Independent Variable: Volume of aluminum foil in cm3

Dependent Variable: Buoyancy Force in number of floated pennies.

ABSTRACT: For this experiment, you shall construct five boats of different volumes, using the same basic design, and determine how the volume of the boat affects the cargo carrying capacity (buoyancy) of the boat.

MATERIALS: 5 aluminum foil squares of the following sizes: 32 cm x 32 cm 28 cm x 28 cm 24 cm x 24 cm 20 cm x 20 cm 16 cm x 16 cm

Ruler Pennies Calculator (Graphing type preferred) Measuring Cup (optional)

APPROACH:

Each individual (or group) will construct 5 different aluminum boats using 5 different sizes of aluminum foil. The volumes of each boat will be calculated and will be plotted on a graph (x-axis) with the number of pennies each boat can float (y-axis) for a total of 5 data points. Each group will try to determine the relationship between the independent and dependent variables.

PROCEDURE:

1) Construct your five boats using the 5 pieces of aluminum foil specified in the materials list.

NOTE: Try to construct the boats for a maximum cargo capacity, using NO scotch tape. 2) Start with the smallest boat. Calculate the volume of each boat hull. Below are two alternative methods you could use. (Or, you could use both methods, and compare your results. Which method is more accurate?)

a.Ruler Method . Use the ruler to measure the length, width, and height of your boat hull. Name: ______Date: ______

. Volume (in cm3 equals length × width × height (each measured in cm). . If parts of the hull have an irregular shape, measure the volume piece-wise. Use triangles to approximate any areas of the hull that are curved or angled. Use rectangular prisms for regular areas of the hull. Calculate the volume of each (imagined) subsection. Add up the volumes of the individual regions to get the total volume for each hull. b.Dry Rice Method . Carefully fill the boat hull with dry rice. The rice should be level with the top of the hull. . Being careful not to damage the hull, pour the dry rice into the measuring cup (or graduated cylinder). . Gently shake the cup (or cylinder) to level the rice. . Read the volume of the dry rice, in ml (1 ml = 1 cm3). This is the volume of your boat hull.

Enter the measurements of your boats in the table below. Multiply the length by the width by the height to calculate the volume of the boats.

Foil Size Length (cm) x Width (cm) x Height (cm) = Volume (cm3)

16 cm x 16 3 ______cm x ______cm x ______cm = ______cm cm

The numbers in the Volume column are for the x-axis on your graph.

3.Measure the buoyancy of each boat hull. a. Carefully float the hull in the container of water. b. Gently add one penny at a time. Note that some boat shapes will be "tippier" than others. For these you will have to pay careful attention to balancing the load (left to right, front and back—or port to starboard, fore and aft, if you're feeling nautical) as you add pennies. c. Keep adding pennies until the boat finally sinks. Count how many pennies each boat could support before sinking (i.e., the penny that sank the boat does not count. d. Repeat this for each boat. Enter the number of pennies floated in the table below. Name: ______Date: ______

Foil Size # of Pennies Floated 16 cm x 16 cm 20 cm x 20 cm 24 cm x 24 cm 28 cm x 28 cm 32 cm x 32 cm

The number of pennies is for the y-axis on your graph.

4. Make a graph of buoyancy, measured in number of pennies supported (y-axis) vs. boat hull volume, in cm3 (x-axis). What do your results tell you about the relationship between buoyancy (number of pennies a boat can support) and volume of the boat hull?

APPLICABLE FORMULAS (FOR FUTURE REFERENCE):

Density = mass per unit volume:

m    (Greek letter Rho): density in kg/m3 V m: mass in kg

V: volume in m3

Buoyancy force = weight of fluid displaced by object:

2 FB  W  Vg FB : buoyancy force in kg m/sec =Newtons W: weight of displaced fluid in kg m/sec2=Newtons  : density of fluid in kg/m3 V: volume of displaced fluid in m3 g: acceleration due to gravity= 9.8 m/sec2 on earth Name: ______Date: ______

Title of Graph (Be descriptive): ______

x-axis – Enter the volume of your boats

y-axis (Dependent Variable) – Plot the number of pennies floated in the boat. Be sure to number consistently and label the scale!

x-axis (Independent Variable) – Plot the volume of each boat. Be sure to number consistently and label the scale! Name: ______Date: ______

Classical Magnet School Physics Lab Rubric

Item Exemplary Acceptable Limited Deficient Clearly, properly, and Clearly and properly Problem statement Problem statement unambiguously stated as a stated as a question. may be unclear or displays a lack of Problem question. Independent Independent and independent and understanding of the and dependent variables Dependent variables dependent variables concepts being explored accurately identified. accurately identified. misidentified or and variables reversed. misidentified. Concise and precise Accurate summary of Stated methodology Stated methodology has Approach summary of methodology methodology to be used contains some little relation to solving to be used to answer to answer problem. inaccuracies or is problem. problem. unclear. Clear and complete, Clear, bulleted, listing of Listing of items may Listing of items used in Materials bulleted, listing of items items used in have some missing performance of the used in performance of performance of the items used in investigation is missing the investigation. investigation. performance of the or contains major investigation. omissions. Accurate, complete, and Numbered step-by-step Step-by-step Procedures outlined do original step-by-step instructions detailing a instructions are not accurately describe Procedures instructions detailing a reproducible method for incomplete or contain what should have been reproducible method for conducting the errors. Method for performed by the group. conducting the investigation. conducting the investigation. investigation would be difficult to reproduce. Pertinent information All information gathered Minor omissions or Incorrect, inaccurate, or gathered is presented is presented in an easy to errors are present in incomplete information Data & without error in an easy to read format (tables when the presentation of is gathered in a read format (tables when appropriate) and clearly information haphazard or hastily Graphs appropriate) and precisely labeled. Graphs have contained in the data, manner due to time labeled. Graphs have descriptive titles including tables, and graphs. mismanagement. Major descriptive titles including all seven applicable labels. omissions and errors are all seven applicable labels. present in the data, tables, and graphs. Mathematical Mathematical Mathematical Inaccurate or manipulation of data manipulation of data manipulation of data incomplete Analysis proceeds in a flawless, proceeds in a logical and may contain minor manipulation of data logical, and progressive progressive manner. errors or omissions. does not demonstrate manner. Derived Derived equations are Derived equations understanding of the equations are presented as presented as functions of may not be presented concepts or data being complete functions of the the investigated variables. as functions of the studied. investigated variables. investigated variables. Units in formulas properly depicted. Conclusions are flawlessly Conclusions are Conclusions contain Conclusions do not synthesized from a proper coherently and accurately minor gaps in reflect a logical analysis. Written synthesized from a proper understanding or synthesis of the data nor statement of analysis analysis. Written misstatements of address the stated Conclusion demonstrates mastery of statement of analysis scientific fact. problem. Errors are not problem’s solution. results properly answers Applicable error discussed. Includes proper error problem. Includes any analysis contains analysis where applicable. applicable error analysis. flaws or is missing.