Best Answer for Children's Game Where Sticks Hold Up Marbles CodyCross TV Station. The word that solves this crossword puzzle is 8 letters long and begins with K.

Activity Summary
Students investigate the meaning of c² in E =mc² by measuring the energy delivered by an object falling atdifferent velocities. Graphing data leads students to understand that Eis proportional to velocity squared, not simply velocity.

Learning Objectives
Students will be able to:

• explain what the c² in E = mc²represents.

• state that kinetic energy is the energy of an object in motion.

• illustrate how kinetic energy can be transferred to other objects.

• understand that the energy delivered by an object in motion isproportional to v², not v.

• copy of the 'Squaring Off With Velocity' student handout (PDF or HTML)
• copy of the 'Data Sheet' student handout (PDF or HTML)
• 1 lb flour in a plastic bag
• plastic pan (about shoebox size)
• two 8-oz plastic cups
• four standard-sized (about 1 cm) glass marbles
• plastic ruler
• meter stick
• plastic spoon
• wood dowel or wood barbecue skewer
• felt-tip pen
• graph paper
• newspaper

Background
Lighthas fascinated scientists for centuries. Galileo Galilei was the first toconsider measuring its speed. In 1676, astronomer Ole Roemer made observationsof the eclipses of Jupiter's moons to demonstrate that light moved at a veryfast—but not infinite—speed. James Clerk Maxwell provided themathematical backbone for electromagnetism and demonstrated that light was anelectromagnetic wave. The squared part of Albert Einstein'sequation heralds back to natural philosopher Gottfried Leibniz, who proposedthat an object's energy is the product of its mass times its velocity squared,not just its velocity. Emilie du Châtelet further championed his ideas.While many of these scientists were innovative thinkers, determination alsoplayed a large part in their achievements. They were willing to challengewidely held beliefs of their day. Their courage and perseverance helped lay thegroundwork for Einstein's eventual connection of mass, energy, and the speed oflight squared.

In this activity, students use a simple model to investigate the relationshipbetween velocity and energy. Their investigation leads them to conclude thatthe energy delivered to a system depends on the velocity squared ofthe impacting body, not simply on the velocity. Students then relate this factto E = mc².

The model uses a glass marble as a falling object that impacts a cup of flour.The impact velocity of the marble is a function of the height from which themarble is dropped. The energy released by the falling marble (its potentialenergy now turned into kinetic energy) is equal to the work done on the flour.The work done on the flour, in turn, is equal to the force (mass xdeceleration) it takes to slow the marble down to zero velocity over thedistance it penetrates the flour.

Four heights are used-10, 25, 50, and 100 centimeters. Students graph thevelocity the marble attains when dropped from these heights against the depthto which the marble penetrates the flour. The depth, in turn, is a measure ofthe energy that the marble delivers. Students can calculate the impact velocityat these four heights by using the equation:

where g = the acceleration due togravity (9.8 m/sec²), and d = the distance the marble falls (in meters)

Key Terms

kineticenergy: Energy of a moving object.

speed: The rate at which an object moves.

velocity: The speed and direction of a moving object.

1. Assemble all the materials needed for the activity.

2. Write E = mc² on the board and ask students whatthe three letters in the equation represent. Emphasize that c stands fora particular constant speed or velocity, that of light in a vacuum.

3. Demonstrate the parts of the apparatus students will use to find therelationship between E and v (a replacement in the model forc). Marbles must be dropped from rest, and the depth to which themarbles penetrate must be measured with a dowel or skewer marked off incentimeters. The depth should be measured from the top of the marble to the topof the flour. The cup must be picked up, and the skewer must be viewed from theside to measure depth accurately. Students should add a half centimeter totheir measurements in order to measure to the marble's center of mass.

4. Organize students into teams. Distribute the student handouts and materials.Assign teams to one of the four heights from which to drop marbles. To ensuredata reliability, have several teams perform the same measurements multipletimes and average the results. As a class data table is going to be made, themore data points the better.

5. Have students place newspaper on the floor, then place their cups filledwith flour in the center of a plastic pan. If students run out of clear area inwhich to drop the marble, have them scoop out the marble(s) with the plasticspoon, use the spoon to refill the cup, tap the base of the cup three times toremove air pockets, and then use the dowel to level the flour to the cup's rim.If students' fingers plunge in to retrieve marbles, they will pack down theflour and their next set of data will be skewed with lower penetratingdistances. Results will also be skewed if they leave air pockets in theflour.

6. Ask students how they might find the velocity of the marble as it hits theflour. When they arrive at the correct mathematical strategy

   have students calculate the velocity values for the fourgiven heights. (Students will need to convert centimeter drop heights tometers.) Students may notice that doubling the height from which they drop themarble does not double the velocity. If the calculations are too rigorous forstudents, provide them with the values for velocity (see Activity Answer) andtell students to square them for the v² column of theirtable.

7. When student teams are finished, create a class data chart on the board andhave students fill it in or have them enter their data into a computerspreadsheet.

8. This is an ideal time to do some data analysis and statistics. Studentanswers may vary quite a bit. For a given distance, ask students which of thedata points are 'wrong' and which ones are 'right.' Discuss the best way toaverage the numbers so students can graph just one depth for each distancedropped. Cross out the two highest and lowest points (outliers) and average therest. Have students average all teams' depth results to determine final classaverages for each depth. Have students enter the results in the depth column inthe 'Velocity vs. Energy Data Table' on their 'Data Sheet' handout.

9. Discuss factors that may cause data to vary, i.e., non-uniform density ofthe flour, problems with measuring depth, variations in tick marks, etc.Emphasize that while accuracy is important, measurements may include a degreeof error. The goal is to see the pattern the data set (that energy isproportional to velocity squared, not velocity).

10. Tell students they will make two graphs, the first with the y-axislabeled Velocity (meters/second) and the x-axis labeled Energy(depthin centimeters). The second graph will have the y-axis labeledVelocity² (meters²/second²) and thex-axis labeled Energy (depth in centimeters). Meters are used onthe velocity axes to simplify graphing. Note that 0,0 must be used as adata point when drawing the curve.

11. Have students plot the first graph. When students have finished plottingpoints, review how to interpolate and draw a curve through a set of pointsinstead of drawing 'dot to dot,' as students will often do. Discuss the factthat a curve shows that the two variables are not directly proportional.

12. Now have students plot their second graph in which the velocity is squared.After students finish their second graph, help them draw a straight linethrough as many points as possible. They should try to have roughly the samenumber of points on either side of their lines. Then have student teams answerthe questions on their 'Data Sheet' handout. Review answers as a class. What isthe most noticeable difference between the two graphs?

13. As an extension, have students use

    tocalculate from what heights marbles would need to be dropped to double thevelocity for each height (beginning with the 10-centimeter height). Havethe students repeat the experiment at this new set of heights (you may need touse very wide-mouth cups in order for students to hit the target flour). Extendthe heights above the flour to 2 meters. Stop taking data when the marble hitsthe bottom of the cup. Direct students to plot this new set of data, compare itto their previous graphs, and find the slopes for each line. Are they the same?Have students explain their results.

Marbles dropped from different heights accelerate toward the surface of theflour, increasing their velocity and kinetic energy as they fall. The kineticenergy that the marble has gained is then transferred to the flour as itplunges in. The depth that the marble reaches in the flour is a measure of thekinetic energy that is transferred to the flour (the energy deforms the flourand makes the marble crater).

Student results may vary due to differences in flour density and errors indropping the marble from prescribed heights. When reviewing the table withstudents, it would be best to eliminate the two lowest and highest values foreach height and average the rest. The summary data plotted should reveal thatenergy is proportional to velocity squared.

Sample Results

Velocity vs. Energy Data Table

The average error of the depth data was about +/- .5 cm.

Student Handout Questions

1. What is the shape of your Velocity vs. Energy graph? The shape of thegraph is a curve.

2. What is the shape of your Velocity²vs. Energy graph? The shape of the graph should be close to a straightline.

3. If a straight line on a graph indicates a direct relationship, is energy(measured by depth) directly proportional to velocity or velocity squared?The Velocity² graph appears to show that energy is proportional tovelocity squared, not velocity.

4. Explain why Albert Einstein wrote E = mc² instead of E= mc. Students may forget that the c is simply the velocity oflight. Einstein wrote c² because E is directlyproportional to velocity squared, not velocity.

Web Sites

NOVA—Einstein's Big Idea
www.pbs.org/nova/einstein
Hear top physicists explain E = mc², discover the legacy ofthe equation, see how much energy matter contains, learn how today's physicistsare working with the equation, read quotes from Einstein, and more on thiscompanion Web site.

Answers from Scientists
www.skirball.org/exhibit/einstein_answers_light.asp
Answers several questions related to light and E = mc².

The Electromagnetic Spectrum
imagers.gsfc.nasa.gov/ems/waves3.html
Describes the electromagnetic spectrum and includes information on visiblelight.

The Ultimate Physics Resource Site
serendip.brynmawr.edu/local/IIT/projects/Glasser.html
Includes physics links and activities.

Books

40 Low-Waste, Low-Risk Chemistry Experiments
by David Dougan. Walch Publishing, 1997.
Includes introductory labs on measurement, density, temperature, relative mass,and more.

Energy by Jack Challoner. Dorling Kindersley, 1993.
Surveys various sources of energy and the ways in which they have beenharnessed.

Light
by David Burnie. Dorling Kindersley, 1999.
Explains many aspects of visible light and other forms of electromagneticenergy.

Stop Faking It!: Light
by William C. Robertson. NSTA Press, 2003.
Provides information and activities to help teachers and students understandlight.

The 'Messing With Mass' activity aligns with the following National ScienceEducation Standards (see books.nap.edu/html/nses)and Principles and Standards for School Mathematics (see standards.nctm.org/document/index.htm).

Grades 5-8
Science Standard
Physical Science

• Transfer of energy

Mathematics Standard
Measurement

Grades 9-12
Science Standard
Physical Science

• Conservation of energy and the increase in disorder

Mathematics Standard
Measurement

Classroom Activity Author

JeffLockwood taught high school astronomy, physics, and Earth science for 28 years.He has authored numerous curriculum projects and has provided instruction oncurriculum development and science teaching methods for more than a decade.

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