Get Into the Game with Team Density!

Transcription

1 Get Into the Game with Team Density! PROBLEM / QUESTION How do mass and volume affect whether an object sinks or floats in water? What is the relationship between density and sinking/floating? PRIOR KNOWLEDGE Students should be able to perform laboratory measurements for mass and volume. SAFETY 8-pound fitness (medicine) balls are heavy; do not drop! MATERIALS electronic balance(s) cork ring(s) metric tape measure(s) (string & a metric ruler/meter sticks can be substituted) 1 set (minimum) of balls: marble ping-pong ball golf ball tennis ball softball billiards cue ball soccer ball racquetball fitness ball (8-pound medicine ball) water bath: large enough to submerge an 8-pound fitness ball (i.e. bucket, sink, garbage pail etc.) PROCEDURE I: Part A Many sporting events (i.e. golf, softball, tennis, etc.) use different types of balls to play each game. Each game uses a specific ball and each game ball tends to differ by weight/mass and size/volume. Your company manufactures sports equipment and is considering a new manufacturing line for the production of round game balls. As such, you have recently been placed on a research team to collect data. Your assignment is to predict, evaluate, and report the mass and volume of several different game balls. Your team will analyze the data to explain how both variables, mass and volume, affect whether a ball sinks or floats in water. Before conducting research and collecting data, scientists often collect qualitative observations of research samples and record a hypothesis. Your first task is to collect qualitative observations of weight/mass and size/volume of different game balls to predict whether each ball will sink or float in water. Obtain a set of game balls as listed in Table 1. 1

2 Table 1. Sample Assignments. Sample # Game Ball 1 Marble 2 Ping-pong ball 3 Golf ball 4 Tennis ball 5 Softball 6 Billiards cue ball 7 Soccer ball 8 Fitness ball 9 Racquetball Lift each ball and arrange them in order of their weight/mass from lightest (least mass) to heaviest (most mass). Arrange the balls in order of their size/volume from smallest to largest. Use your qualitative observations to predict whether each ball will sink or float in water. Record all predictions in Table 2. Briefly describe the reasoning behind your predictions. Table 2. Sample Predictions & Observations: Sink or Float? Sample # Type of Ball Prediction Sink or Float? (S or F) 1 Marble 2 Ping-pong ball 3 Golf ball 4 Tennis ball 5 Softball 6 Billiards Cue ball 7 Soccer ball 8 Fitness ball 9 Racquetball Observation Sink or Float? (S or F) 2

3 PROCEDURE I: Part B Your instructor will provide the mass of the fitness ball and assign your group three or more additional balls to investigate. Record the mass of each ball in Table 3. The volume of each ball can be determined by measuring the circumference and dividing by 2π to obtain the radius. With the radius you can calculate the volume using the formula shown below. Record the volume in Table 4. using the units of cm 3 (cubic centimeters). Record your circumference data and show your work for calculating the volume of one of the balls here. Teacher Check 3

4 DATA AND OBSERVATIONS I Table 3. Mass Measurements (grams). Type of Ball Marble Ping-pong ball Golf ball Tennis ball Softball Billiards Cue ball Soccer ball Fitness ball Racquetball Group 1 * * * * * * * * * 2 3 Average Mass Table 4. Volume Measurements (cm 3 ). Type of Ball Marble Ping-pong ball Golf ball Tennis ball Softball Billiards Cue ball Soccer ball Fitness ball Racquetball Group 1 * * * * * * * * * 2 3 Average Volume To test the sink or float? predictions your team made in Table 2, place each assigned ball into water and record the results in Table 2. 4

5 RESULTS AND ANALYSIS I Patterns in the data Compare the predicted order of Mass from page 2 and the actual mass measurements from Table 3. Were there any balls that were not what you expected? Briefly explain any discrepancies. Compare the predicted order of Volume from page 2 and the actual volume measurements from Table 4. Were there any balls that were not what you expected? Briefly explain any discrepancies. From the data collected in Table 2, compare your team s qualitative sink or float predictions to your team s sink or float observations. Were your predictions accurate? Which balls may have surprised you? Briefly explain any discrepancies. Choose two balls (one that sinks and one that floats) that have approximately the same mass. How does the volume of these two balls compare? Based on these results, how does volume affect whether a ball sinks or floats? Choose two balls (one that sinks and one that floats) that have approximately the same volume. How does the mass of these two balls compare? Based on these results, how does mass affect whether a ball sinks or floats? 5

6 Can you use either mass or volume alone to determine whether a ball or object will sink or float? Briefly explain. PROCEDURE II Density is a measure of the relationship between mass and volume. The density of a ball can be determined by measuring how much mass is present in a given volume. Density is typically reported in units of for solids &/or for liquids. The formula for density is shown below. Use the average mass and volume values from Tables 3 and 4 to calculate the density of each ball. Show one calculation in the space below and record the density of each ball in Table 5. Table 5. Density Determinations (. Type of Ball Marble Ping-pong ball Golf ball Tennis ball Softball Billiards Cue ball Soccer ball Fitness ball Racquetball Density 6

7 RESULTS AND ANALYSIS II Patterns in the data From the density determinations in Table 5, arrange each ball from least to most dense. How does the density of the balls that sink compare to the densities of the balls that float? Is there a pattern? Briefly explain your answer. How do the densities of the balls that sink compare to that of water (0.998 at 20 C)? How do the densities of the balls that float compare to that of water (0.998 at 20 C)? DISCUSSION Write a brief summary of your findings explaining how mass and volume affect the density of a ball. Furthermore, explain how density affects whether an object sinks or floats in water. The density of water at 20.0 o C is What mass is necessary to sink a fitness ball in water at 20.0 o C? The mass of fitness balls can vary from 8 pounds to 16 pounds, while the circumference and thus the volume remain the same. Hint #1: 1 pound = 453.6g. Hint #2: see Table 4. Show calculations! 7

8 GOING FURTHER A person hands you a golden-colored cube and wants you to buy it for $100 because they claim it is gold! You refer to your old geology text to look up gold in the mineral table, and find that its density is You measure the cube and find that it is 2cm on each side and weighs 40.0g. What is the density? Is it gold? If not gold what volume would you expect a 40.0g cube to be? Show your work! When you heat air it becomes less dense (this is how hot air balloons work). By heating the air you are not changing the amount of air (mass of air), so why does its density decrease? Your explanation should describe what is happening at the particulate level. REFERENCES Adapted from Comparing Densities R. H. Moyer, J. K. Hackett, S. A. Everett, Flinn Scientific Catalog/Reference Manual (2009). 8