Sink and Float - homepages.math.uic.edu

1 Sink and Float , page 1 of 12 OverviewWhy do some objects sink and others Float inwater? Why can an egg which sinks in water floatif you add a few teaspoons of salt? Why does agreat ocean ship like the Queen Mary Float if it ismade of steel, while a piece of steel sinks? AsPiaget1 pointed out, this question is difficult forchildren to answer because they try to oversimplifythe problem. We saw this earlier when we studiedvolume in Marshmallows vs. Containers. Wenoted then that the children often say the tallestglass has the greatest volume of water, ignoringthe other two dimensions forming the cross-sectional area of the glass. If an object sinks andthe child is asked why, the answer would be asPiaget noted, Because it is heavy.

2 If it floats,then the response is That one swims because it islight. Sometimes the children answer that itfloats Because it is big and sometimes they sayit goes to the bottom Because it is big. Theseconfused responses were given by children whomTeacher Lab DiscussionSink and FloatPiaget interviewed whose ages ranged between 5and 12. Why? What are the children doing wrong?They are simplifying the problem so that they onlyuse one variable, either mass or volume, to describewhether an object sinks or floats. As we shall see,it is necessary to use both variables to understandthe situation properly, just as it is necessary toinclude both the height and the cross-sectionalarea of an object to determine its can t really blame the children for this lack ofinsight because they have never done an experimentwhich exposes and contradicts their biases.

3 OurSink and Float does just do we express this problem in the scientificlanguage of variables? The type of object is themanipulated variable (Question 1). Whether itsinks or floats is the responding variable (twovalues, S and F) (Question 2). The type of liquid5 6 7 MiddleMass/Volume InvestigationFigure 1 Sink and Float , page 2 of 12is held fixed during the experiment. To distinguishbetween materials, we need two quantitativevariables: mass and volume. Therein lies theproblem for the children. They have to identify theobject by its mass-volume relationship. They plotthe mass-volume relationship of all the objects onone graph and see if they can predict which objectswill sink and which will , Data Table, and GraphEach pair of children is given several objects alongwith some water.

4 They have to measure andrecord the mass and volume of each. Then theydetermine which ones sink and which ones Float inwater. The children should make a fairly detailedpicture of this, like the one shown in Figure 1. Allthe variables are identified: T for type of object,M for mass, V for volume, S for Sink, and F forfloat. The apparatus is also clearly shown. Withthis picture someone can easily repeat list of the objects we use at UIC are shown inFigure 2. Some of these objects the spheres andclay are part of the TIMS package of can easily dig up a rock and ask your colleaguesto save their fine wine of the most important items, however, is theparaffin block. This should be available in blockform from your local supermarket. The reasonparaffin is so important is that you want at least oneobject which is heavier than most of the otherobjects but which still floats.

5 This will causeunending confusion for the children because theythink heavy objects sink. Yet here we have one ofthe heavier objects floating. Our paraffin blockhas cm cm cmand has a volume of approximately 109 cc. It isimportant that the children measure the block slength, height, and width to the nearest should use their calculators to determineaccurately the block s , make sure that one of the objects that sinkshas more volume than at least one of the objectsthat floats. In our case the rock sinks even thoughit has more volume than the wood sphere. Again,this should raise questions because childreninherently think that objects Float because theyhave more volume. Here is one that doesn measure the mass of water, fill the graduatedcylinder with 100 cc of water (V) and measure itsmass, M full = M water + M cylinder.

6 Then, empty thewater and measure the mass of the empty graduatedcylinder, Mcylinder. The mass of the water isM water = M full M cylinder when the volume of wateris 100 children carefully measure M and V for eachobject and enter that information in the data then record whether the object sinks or floatsin the last column of the data children now plot the mass-volume curve forevery substance including water. The childrenshould have done the TIMS experimentTable IObjectMass in gmVolume inccSink or Floatrock6523 Sclay4027S1" steel " glass sphere2 " plastic sphere1 " wood 2 Sink and Float , page 3 of 12volume. After drawing in the line for water youcan ask, Is its volume less than 20 cc? If it is, itwill sink; if not, it will Float .

7 If its volume is 16 cc,then you can plot the (V,M) data point and see thatthe object sinks. This is illustrated in Figure similar argument holds if we give you onlyvolume information. We explore these ideas in thefirst few comprehension happens if you change the type of liquid?Although we could redo the experiment with adifferent liquid, we can also argue inductively asfollows. If the object s mass-volume curve liesabove the line for the new liquid, the object willsink; and, if it lies below, it will Float . Therefore,all we have to do is find (V,M) for the new liquid,plot its mass-volume line, and see where the (V,M)point for the object lies relative to the new liquidline. For example, if the new liquid has a mass of24 grams when its volume is 14 cc, then its mass-volume line, as shown in Figure 4, lies above thedata point for the object.

8 Therefore, since theobject now lies below the liquid line, it floats in thenew liquid! It is this kind of analysis the childrenshould carry out when answering thecomprehension vs. Volume before Sink and Float so theyknow that each substance has a unique (V,M)curve passing through (0,0) (Question 3). Theyalso know that the best fit mass vs. volume curve(Question 4) is a straight line. Since that is true,the children only need one data point (along with(0,0) for each substance. The children can theneasily draw the line through the data point and theorigin, as shown in Figure 3. Have them label eachcurve, as we have done, placing an S or F next tothe type of children should recognize the emergingpattern. The curves of all objects that sink in waterlie above the curve for water.)

9 The curves ofobjects which Float lie below the curve for each curve is determined by the relationshipbetween mass and volume, both mass and volumedetermine whether an object sinks or floats inwater, not just mass or volume. If we describe anobject with a mass of 20 gm and ask whether itsinks or floats, you should answer, I have no is its volume? As illustrated in Figure 4, theobject could lie at any point along the horizontalline drawn which starts at (0 cc, 20 gm). Youcannot plot the point because I did not tell you theFigure 3 Figure 4048121620242830048121620242630M in gmV in ccNewLiquidWaterObjectSINK IN WATERFLOATIN WATER020406080100 120 1400102030405060708090100110120130140 Cork (F)Wood (F)Paraffin (F)WaterClay (S)Plastic (S)Rock (S)Steel (S)V in ccM in gmGlass (S)Sink and Float , page 4 of 12 Liquids other than water are often messy to syrup is an example of a liquid that has its (V,M) line above that for water.

10 But an object placedin Karo syrup gets yucky. Our suggestion is for theteacher to do a classroom demonstration withKaro syrup. The ratio of M/V for Karo syrup is7gm/5cc. The children can plot the Karo syrupline and see if any of the objects now Float insteadof sinking. Then let them place the object in thesyrup and see if they are correct. They will find theplastic object which sank in water now floats inKaro syrup. We return to this idea in thecomprehension questions by studying a type of object could be another liquid ratherthan a solid. For example, what happens when youdrop corn oil (nice and yellow) into water? Havethe children determine the (V, M) curve for cornoil. They will find that it lies below the water , corn oil floats in water.