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INQUIRY PHYSICS inquiryphysics.org A Modified Learning Cycle Curriculum by Granger Meador, ©2010 Unit 6: A Property of Matter (Mass) Teacher’s Guide Student Papers Sample Notes 6 A Property of Matter (Mass) Teacher's Guide Inquiry Physics Key Concepts W eight is the result of gravity acting on an object. Mass is the quantity of m atter in an object and is responsible for its inertia. Acceleration is inversely proportional to the m ass being accelerated when a constant force is applied. Student Papers Lab A: The Inertial Balance Metal Plates Version Cylinder Version Reading: Mass - Not A W eighty Matter W orksheet: “The Vom it Com et” Lab B: Mass and Acceleration Air Track Version Air Track Lab Report Version Dynam ics Cart on Floor Version Dynam ics Cart and Table Pulley Version Introduction To this point in the course, the concept of m ass has not been m entioned, and if brought up by a student, it has not been pursued. Hence the title of the unit is “A Property of Matter” and not “Mass”, as you do NOT want to give them the idea of m ass until the discussion phase of 6 Lab A. Using weight up to this point is justified by students' grasp of that concept from life experience: weight is how heavy an object is. Their conceptual understanding of m ass is often quite lim ited and flawed. This investigation forces the students to address the m ass concept, which in turn dem ands a better definition of weight. The investigation also has students discover the relationship between m ass and acceleration when the applied force is constant. Take care to also NOT invent F=m a in this investigation, and for now ignore the issue if students bring it up. That law will be invented in the next investigation, using both Unit 5 Lab B and Unit 6 Lab B. LAB A: THE INERTIAL BALANCE Exploration Equipm ent for each group (of 3 to 4 students): Inertial balance of either style: one style has an attachable cylinder, another has m etal pieces that clam p onto the balance (you can also just add sm all C-clam ps to any style balance, or you can m ake your own balance with a shielded saw blade (see NASA activity in the “acrobat/Other Resources” subdirectory on the Inquiry Physics CD; use the appropriate version of the lab, m odifying as needed C-clam p thin board to protect desk/counter surface stopwatch ruler 500 g m ass and m asking tape (or a big clam p) for single-cylinder balances IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 2 O F 12 I’ve seen and used two styles of inertial balance. One uses a m etal cylinder that inserts in a hole in the pan, while the other clam ps m etal pieces onto the pan. I’ve included a version of the lab instructions for either style, and you can even m ake your own version as shown in NASA’s Inertial Balance lab on the Inquiry Physics CD in the “acrobat/Other Resources” subdirectory. Just m odify the W ord or W ordPerfect version of m y lab to m atch your equipm ent, including playing around with how far to have the students pull aside the pan and how long to tim e it to find out what works best for you. Tim ing the unloaded balance when the springs are stiff can be a challenge for the students, and they m ay com plain about that. Insist that they devise a procedure to get as accurate a count as possible. The actual num bers they obtain really are not very im portant; the crucial bit of data is that the counts go down as m ore "weight" is added to the balance. (One m ethod of obtaining an accurate count for the unloaded balance is to attach an index card to one side and have it oscillate in front of a m otion detector with com puter interface; a d vs. t graph of the m otion can be studied to count the oscillations. Or sim ply have it lightly tap against a piece of paper held up beside it to facilitate counting, although this can dam p out the m otion.) The Idea Inventing the concept of m ass and the differences between weight and m ass require class discussion. Part of that discussion focuses upon extracting key ideas from investigations 3 through 5. This lab is a wonderful opportunity to confront students with a phenom enon that cannot be explained by weight, but only by m ass. W eight cannot directly affect horizontal m otion (a concept the students should have grasped in their study of projectile m otion), so it cannot explain why loading the balance up causes it to oscillate m ore slowly. Only m ass can explain this, and you should allow the idea of m ass to be invented by the students; do NOT accept flawed reasoning on their part to bring weight into the answer, and do NOT sim ply give them the idea of m ass. They will be able to construct the idea given tim e and a thorough class discussion of the questions on the lab. Also, do not attem pt to introduce the concepts of frequency or period in this lab - focus on the m ass concept. Sample Answ ers for Lab A: The Inertial Balance 1. W hat is the direction of the acceleration vector of a falling object? It is downward (toward the center of the earth). 2. W hat is needed to cause an object to accelerate? An unbalanced force. (The students know about vectors, so you can stress the importance of an unbalanced force here.) 3. W hat force causes the acceleration of a falling body? Gravity causes the acceleration of a falling body. (Technically, the acceleration arises from the interaction of the object and the gravitational field, but such distinctions are not important here.) Now the investigation introduces the concept of w eight, taking it beyond the idea of how heavy an object feels. The students need to realize that w eight is a vector that points dow nw ard, a key idea if they are to properly interpret the inertial balance data. W eight pushes dow n, w hile the spring force on the balance is sidew ays, and the dow nw ard w eight vector is cancelled by an upward force from the platform on the balance. IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 3 O F 12 4. The term that is used for force due to gravity on any object is w eight. So the force due to gravity on you is your 5. weight. Sum m arize the results of the lab. (How did the added objects affect the num ber of oscillations?) Adding objects decreased the number of oscillations. 6. W hat is the first explanation you can think of for this data? answers will vary (M any students w ill say that the increased w eight slow ed the balance; that will suffice until they are confronted w ith questions 7 and 8 and hopefully realize that explanation is invalid.) 7. W hat effect does gravity have on the m otion of the balance? Think about the direction of gravity and the direction the balance m oved before answering. Explain your answer com pletely. Gravity cannot affect the motion of the balance, because vertical forces cannot affect horizontal motion (or because the force of gravity is being cancelled by the upward push of the table/countertop/balance platform). 8. Given your answer to question 7, what effect does w eight have on the m otion of the inertial balance? Explain your answer com pletely. Weight does not affect the motion of the balance, because weight is due to gravity and gravity has no effect on the motion (or because weight is a vertical force that cannot affect horizontal motion, or because the weight is being cancelled by other forces). 9. Your answers to questions 7 and 8 m ay have invalidated your initial response to question 6. If your answer to question 6 is no longer valid, give the correct explanation below: A greater mass will oscillate more slowly (greater mass accelerates less). IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 4 O F 12 Expansion of the Idea After com pleting lab A, it is tim e to define weight and m ass in the students' notes and practice with the various related units, equations, and conversions. You should also connect the idea of m ass with inertia. See the sam ple notes for m y approach, although I’ve outlined the m ajor m ethods below. M ass, W eight, Volume, Density Concepts You can define each of the above with the students, perhaps indicating com m on units of each. Then practice the distinctions by taking a Nerf ball and having the students consider various situations in a signal exercise: Describe the situation, give the students a m om ent to consider, and then direct them to all sim ultaneously show on their raised fingers how m any of the four quantities changed. Discuss the answers with them , focusing on the students who gave im proper signals. Situation: Crush the Nerf ball in your hands Say that you are taking the ball to the m oon Back on earth, toss the ball in the air Say you've ripped off part of the ball and thrown that part away Num ber of Changes 2 1 0 3 Mass Effect no change no change no change sm aller W eight Effect no change sm aller no change (ignore slight variation in gravity at different heights) sm aller Volum e Effect sm aller no change no change (ignore m inute air resistance distortions) sm aller Density Effect higher no change no change (ignore m inute air resistance distortions) no change M ass and W eight Calculations You can introduce the equation F g=m g (be careful NOT to expand this equation into F=m a yet!) by hanging a one kilogram m ass on a large newton scale. The students will notice that it weighs slightly less than 10 N, and a bit of prom pting will lead them to: 9.8 N = 1 kilogram which is im possible, for weight cannot equal m ass. So a correction can be inserted: 9.8 N = (1 kilogram ) (?) and they will quickly suggest that the m issing factor is a 9.8, as in 9.8 m /s 2: 9.8 N (1 kg) (9.8 m /s 2) and you can point out that translates to F g=m g, using F g for weight, m for m ass, and g for the acceleration due to gravity. (I avoid using W for weight since later we’ll use that sym bol for work. And using F g here m akes the leap to F=m a in the next unit that m uch easier.) Then discuss the units of weight and m ass, and use your own weight to m ake the following calculations, while the students duplicate your procedures in their notes, using their own individual weights. (Since they are each doing their own work, they will not feel threatened by having their weight publicized.) I weigh pounds. 170 pounds I weigh newtons. 170 lb * (4.4482 N/lbs) = 756.19 N = 756 N My m ass is kilogram s. m = F g/g = (756.19 N)/(9.8 m /s 2) = 77.162 kg = 77.2 kg My m ass is slugs. m = F g/g = (170 lbs)/(32.2 ft/s2 ) = 5.2873 slugs = 5.29 sl IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 5 O F 12 I extend into how weight varies with location and m ass varies with speed (due to special relativity), using a PowerPoint you will find in the PowerPoint directory on the Inquiry Physics CD-ROM. I also like to show clips from an old 1994 video, W e’re Go for Launch to Zero-G , about the effects of “weightlessness” on the hum an body and I show clips of folks and cats aboard the old Vom it Com et zero-g sim ulator aircraft. Do an online search and you can find lots of clips. I’ve included a worksheet on that plane. Here is how I introduce the idea that weight varies with location: Location Chicago Panam a Canal North Pole Space Station Moon surface g 9.803 m /s2 9.782 m /s2 9.832 m /s2 8.71 m /s2 1.62 m /s2 My W eight There F g = m g = (77.2 kg)(9.803 m /s 2) = 756.79 N F g = m g = (77.2 kg)(9.782 m /s 2) = 755.17 N F g = m g = (77.2 kg)(9.832 m /s 2) = 759.03 N F g = m g = (77.2 kg)(8.71 m /s2 ) = 672.41 N / F g = m g = (77.2 kg)(1.62 m /s2 ) = 125.06 N / / 4.4482 / 4.4482 / 4.4482 4.44822 4.44822 N/lb N/lb N/lb N/lb N/lb = = = = = 170. lbs 170. lbs 171 lbs 151 lbs 28.1 lb Sample Answ ers for the Reading: M ass - Not A W eighty M atter 1. W hat is an unbalanced force? W hat does an unbalanced force do to an object? (Be exact.) An unbalanced force is one which is not balanced by another force. It causes an object to accelerate. (Do not accept "move" in place of accelerate.) 2. Victor Vector weighs 650 newtons, while Velm a Velocity weighs 750 N. W ho has greater inertia? Describe your entire train of logic which led you to that conclusion. Velma has more inertia, because she weighs more and thus has more mass and thus has more inertia. 3. Suppose you were in a w eightless environm ent. If you looked in a m irror, would you appear any thinner? Justify your answer. answers will vary (The simple answ er is that you w on’t be thinner since your mass is unchanged. But if you’ve shown them some online clips about the effects of zero-g on the body, they may know that you w ould appear thinner around the middle, as the body's organs tend to shift upw ard into the abdomen in a w eightless environment and the spine lengthens by an inch or tw o, w hile you appear fatter in the face, since fluids shift into the face and make it puffy.) 4. Under what condition did Einstein say the m ass of an object would increase? Mass increases as speed increases (near light speed). 5. Describe a situation in which knowing the m ass of an object would be preferable to knowing its weight. Be specific and creative! Explain your answer, and be careful not to confuse m ass with volum e. answers will vary (Do not accept answers which confuse mass w ith w eight, or mass w ith volume. Correct answ ers w ill often deal w ith motion in space or w ith horizontal motions in general.) IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 6 O F 12 Sample Answ ers for W orksheet: The “Vomit Comet” 1. The plane traces a parabola, so for half of the “weightless” or “zero-gravity” period the plane is actually rising through the air, and falling during the other half. Draw the vertical displacement, velocity, and acceleration graphs for the occupants during the “weightless” sensation period, recalling that they are not really weightless, and are both rising and falling. 2. Suppose during one arc the occupants are “weightless” for a total of 20.0 seconds. So they spend 10.0 s ascending and 10.0 s descending. Using the true acceleration of gravity of 9.80 m/s 2, calculate how far the plane would fall in meters and then in feet (1 m = 3.281 ft) from vertical rest during the descending half of its arc: Fall in meters (m): Fall in feet (ft): show your work = 490. m = 1610 ft 3. Let’s suppose that an occupant’s pre-flight weight was 175 pounds. Compute his mass in slugs, using F g = mg where g is 32.2 ft/s2 . Stay in US Customary units throughout your calculation – do NOT convert to SI/metric units. 4. Now convert the occupant’s mass into kilograms, using the US-to-metric mass conversion factor in your notes: IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 7 O F 12 Special Relativity Students are fascinated by the bizarre effects of extrem e speeds due to special relativity (increasing m ass, tim e slowing down, objects becom ing thinner in the direction of m otion). I like to introduce special relativity with the PowerPoint on the CD and excerpts from a funny old 1957 film by Dr. Irwin Moon, The Mystery of Time, which you m ight be able to to get from www.archive.org, but be aware that Dr. Moon had a religious m otive and was covering m ore than special relativity; we only watch 16:42-23:00 of that video. I refer students who want to delve m ore into special relativity and why it occurs to their textbook for details. If som eone really gets into the topic, I loan them Martin Gardner’s great book on the topic, Relativity Simply Explained (form erly titled Relativity for the Million). Here is how one quantifies the concept from the reading that m ass varies with speed: where c=3x10 8 m /s (186,000 m i/sec). Speed 0 Concorde (m ach 2; 1354 m ph; 605 m /s) Voyager Probe (37240 m ph; 16648 m /s) one-half light speed three-quarters light speed 99% of light speed light speed % of m ass increase 0 0.0000000002% 0.000000154% 16% 51% 600% infinite; m atter cannot achieve light speed ("warp one") LAB B: ACCELERATION vs. M ASS Here the students explore how m ass, rather than force, affects acceleration. Make sure the results are acceptable, for in the next investigation you will use the results of this lab and 5 Lab B to invent F=m a. Equipm ent for each group (of 3 to 4 students): Air track version: 1.5 m or longer air track with end pulley 2 red 300 g gliders and 1 gold 150 g glider with velcro on their bum pers (or carefully brought together on an active air track and secured with paperclips) stopwatch string/fishing line hanging weight holder Dynam ics cart on floor version: dynam ics cart (taping weights onto each cart beforehand to m ake it a convenient m ass can save lab tim e) 5 N and/or 20 N spring scale m eterstick long spring (perhaps cut a worn-out wave dem onstrator spring to 50 cm ; avoid Slinkies, which are too large, and rubber bands, which don't have a constant force/stretch ratio) tape (or thum btack or sm all nail) to secure spring to m eterstick enough 1 kg m asses to bring loaded cart up to 6 kg Dynam ics cart and table pulley version: dynam ics cart (taping weights onto each cart beforehand to m ake it a convenient m ass can save lab tim e) table pulley string/fishing line hanging weight holder m eterstick enough 1 kg m asses to bring loaded cart up to 6 kg IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 8 O F 12 It is best to begin the lab with the largest m asses and work downward, especially if using the dynam ics carts on the floor, where holding the spring force constant is difficult with a low-m ass cart. The air tracks will usually give good results, but the dynam ics carts are m ore problem atic, especially when used on the floor. You m ay need to group data, drop highs and lows, and have them graph the class average, or even send them back to recollect data if it is too poor the first tim e. For the air track and dynam ics cart with table pulley versions, keep the pulling force sm all so that the later low-m ass runs don't becom e too fast for the students to tim e. Am ong other variants is using a dynam ics cart on a special grooved track. Som e schools use photogates, sonic rangers, and the like to analyze the m otion. You can m odify the W ord or W ordPerfect versions of the student handouts on the CD-ROM to m atch your equipm ent. Lab Report Option At this point, you m ay want to have the students write up their own lab report, with plenty of guidance and support from you as to the proper form . I’ve included a lab report handout I use with m y AP Physics B students when they do the air track version of the lab. I have their groups confer to answer the initial questions on the sheet and then call groups aside to ask each student about the lab to ensure they have a workable procedure and understand what is going on If you go with the lab report option, here are the correct answers to the questions I ask of them before allowing them to collect the data: 1. W hat are the independent and dependent variables? M ass is the independent variable; acceleration is the dependent. (Time is also technically a dependent variable here.) 2. W hat quantities will you hold constant, at what values, and how will you accomplish that? Force w ill be held at [w eight of w eight holder in new tons] Distance will be held at [0.9 m or w hatever is practical] Initial speed w ill be held at zero 3. W hat data must you collect, and what standards of reproducibility will you enforce? (How many trials will you take? How close must the data be before continuing to another trial?) Collect time for each run, requiring that there be three runs within 0.1 s for each glider set. 4. W hat is the best order to the data collection which will minimize human error? Use the largest trains first, since they have the most mass and w ill be slow er and easier to time, saving the short trains for last. After the Sam ple Answers on the following pages, I’ve included the grading rubric I use for the lab report. IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 9 O F 12 W hat if my students do not have access to a computer or calculator for graphing? Many of the graphs in this curriculum are linear, so students can sim ply plot the points by hand and eyeball a best-fit line. Careful plotting and drawing of the best-fit line will yield equations with useful slope values. However, in this lab they face an inverse relationship, and hand-drawn hyperboles are seldom accurate. If your students need to construct graphs by hand (or if the graphing software cannot handle inverse fits), that need not prevent them from decisively determ ining the num erical relationship between acceleration and m ass. They’ll just need to draw two different graphs - one to determ ine the type of relationship and the second to find the num erical values in it. You will probably need to lead them through the process with sam ple data or a class average. 1. Plot the data and note the shape of the best-fit curve and its general meaning. First have the students graph acceleration vs. m ass (acceleration on the y-axis and m ass on the x-axis). Have them eyeball a best-fit curve to the data points, which should yield a reasonable hyperbole with the axes as asym ptotes. You will then need to ask them to identify the m athem atical m eaning of that shape, or lead them to realize that it im plies that acceleration is inversely proportional to m ass. 2. Re-compute for the discovered relationship and re-plot accordingly. The next step is to test for that inverse relationship. The students will now com pute the inverse of the m ass for each part of the experim ent. Then have them graph acceleration on the y-axis and 1/mass on the x-axis. If their data is good, the points should plot out in a roughly straight diagonal line. 3. An inversely proportional relationship will yield a straight line on the second graph. Ask the students what the line m eans. It m eans that acceleration is directly proportional to the inverse of m ass, which is the sam e thing as saying acceleration and m ass are inversely proportional. Have them eyeball a best-fit line for the second graph. (Here is useful to rem ind them that a best-fit line need not hit even a single plotted data point nor go through the origin. A best-fit line runs through the “m iddle” of the data point distribution.) 4. Using the slope of the best-fit line to obtain the relationship. Once the students have drawn the best-fit straight line, have them com pute its slope. The resulting equation will be a = k (1 / m) + b where a is the acceleration, k is the slope, 1/m is the inverse of the m ass, and b is the graph’s y-intercept. Voila! They now have the sam e equation a fancy com puter or calculator would have calculated when form ing a best-fit hyperbole to the original acceleration vs. m ass graph. 5. Use the results. Now the students should be able to give fairly decent answers to the questions in the lab about the equation of the graph and m ake decent predictions about the acceleration for various m ass values. They m ust use the second graph (the linear one of a vs. 1/m ) to obtain decent predictions, for the hand-drawn best-fit hyperbole on the first graph will likely be inaccurate. Do NOT assum e students will easily follow all of this! A com m on error is thinking that the second graph indicates acceleration and m ass are directly proportional, ignoring the inversion of m ass and its physical m eaning. Som e students will sim ply go through the drill of m aking the graphs without thinking about what they are doing, unless you question them verbally or in written form . IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 10 O F 12 Sample Answ ers for Lab B: Acceleration vs. M ass 1. W hat happened to the acceleration of the gliders as you increased their m ass? The acceleration decreased as the mass increased. 2. Describe the shape of the curve on your graph. W hat kind of function does it represent? The shape was hyperbolic, representing an inverse function. 3. That shape/function allows you to predict how m ass affects acceleration. If the m ass was cut to one-fourth of its previous value, what would the new acceleration be? The acceleration would quadruple. 4. W rite the full equation for your graph. Rem em ber to substitute the proper variable nam es for y and x and to indicate the correct values for any constants. Rem em ber to round off values for significant figures. a=x/m (x w ill vary, and should be close to the amount of force used, but don't point that out to the students yet; if x isn't close to the force used, check for errors in the data) 5. Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration for two values of m ass, one four tim es larger than the other. W rite down those values and then com pare them m athem atically in a ratio. (Divide the larger acceleration value by the sm aller one.) W rite your ratio down too, using 3 significant figures. Accel. of kg = m /s2 Accel. of kg = m /s 2 Ratio = to 1 answers will vary; the ratio should be close to 4 to 1 6. Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you answer this question. Notice how we changed the m ass.) The ratio should be 4 to 1. 7. W rite in words the m athem atical relationship you have found between m ass and acceleration. Mass and acceleration are inversely proportional. (Do NOT accept "indirectly" in place of "inversely".) IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 11 O F 12 Grading Rubric for Lab Report Option for Lab B: Acceleration vs. M ass I copy this page and cut it in half so that I have one strip for each student’s paper. Then I fill out the rubric as I grade the lab and staple it on front of the report for return to the student. 6 Lab B: Acceleration vs. M ass Lab Report Grading Rubric (45 points) 6 Lab B: Acceleration vs. M ass Lab Report Grading Rubric (45 points) ___ General legibility; if typed, doubled-spaced (2 pts.) ___ General legibility; if typed, doubled-spaced (2 pts.) Purpose (5 points) Purpose (5 points) ___ Correct statem ent of relationship under study (4 pts.) ___ Correct statem ent of relationship under study (4 pts.) ___ Spelling, gram m ar, usage (1 pt.) ___ Spelling, gram m ar, usage (1 pt.) Procedure (15 points) Procedure (15 points) ___ Major equipm ent identified (1 pt.) ___ Major equipm ent identified (1 pt.) ___ Leveling of track m entioned (1 pt.) ___ Leveling of track m entioned (1 pt.) ___ Independent variable of m ass identified (1 pt.) ___ Independent variable of m ass identified (1 pt.) ___ Dependent variable of acceleration identified (1 pt.) ___ Dependent variable of acceleration identified (1 pt.) ___ Force held constant; value shown (2 pts.) ___ Force held constant; value shown (2 pts.) ___ Distance held constant; value shown (2 pts.) ___ Distance held constant; value shown (2 pts.) ___ Initial speed specified as zero (1 pt.) ___ Initial speed specified as zero (1 pt.) ___ Three trials within 0.1 s m entioned (1 pt.) ___ Three trials within 0.1 s m entioned (1 pt.) ___ Specified m ass decreased to im prove tim ing (1 pt.) ___ Specified m ass decreased to im prove tim ing (1 pt.) ___ Spelling, gram m ar, usage (1 pt.) ___ Spelling, gram m ar, usage (1 pt.) Data (8 pts.) Data (8 pts.) ___ Data table intelligible and com plete (2 pts.) ___ Data table intelligible and com plete (2 pts.) ___ Units shown on data or in header rows (1 pt.) ___ Units shown on data or in header rows (1 pt.) ___ Graph with correct best-fit curve (5 pts.) ___ Graph with correct best-fit curve (5 pts.) Conclusion (15 pts.) Conclusion (15 pts.) ___ Verbal statem ent of relationship m á 1/a (5 pts.) ___ Verbal statem ent of relationship m á 1/a (5 pts.) ___ Equation w/ proper variables, sig figs, values (6 pts.) ___ Equation w/ proper variables, sig figs, values (6 pts.) ___ System atic errors ID e.g. friction (3 pts.) ___ System atic errors ID e.g. friction (3 pts.) ___ Spelling, gram m ar, usage (1 pt.) ___ Spelling, gram m ar, usage (1 pt.) TOTAL: __________ TOTAL: __________ IN Q U IRY P H YSICS T EACH ER 'S G U ID E FO R U N IT 6: A P RO PERTY O F M ATTER ( M ASS ) P AG E 12 O F 12 INQUIRY PHYSICS A Modified Learning Cycle Curriculum by Granger Meador Unit 6: A Property of Matter (Mass) Student Papers ©2010 by Granger Meador inquiryphysics.org 6 A Property of Matter Nam e Lab A: The Inertial Balance Metal Plates Version Introduction When you step on a bathroom scale, you measure your weight. Many purchases we make, such as meat and vegetables, are made in terms of weight. Bridges specify the maximum weight they can support. Trucks are rated according to hauling weight limits. When a truck smashes into a building or through a wall or fence, what property of the truck causes the damage? (Speed is not a property of an object, merely a measure of its movement.) In this investigation, we will identify a property of matter which is sometimes confused with weight. The Inertial Balance Clamp the inertial balance to the table with the C clamp as shown in the figure below. Place a protective piece of wood between the balance and the table to prevent scratching. Set the balance in oscillation by pulling it horizontally 5.0 centimeters to one side. Count the number of complete oscillations (a swing from the starting position, through the resting position, and back to the starting position) occurring in fifteen seconds. (You may need to let the balance lightly strike a piece of paper in order to count the number of swings.) Repeat the exercise once more, and record your data in the table. Next, load the balance with one piece of metal, securing it with the eyebolt keeper. (Pass the nut of the keeper through the hole in the platform and place the metal piece above the pan but below the collar on the eyebolt. Tighten the wing nut down onto the collar while the nut is pressed against the side of the hole so that the metal piece is held securely.) Repeat the measurements you made in the previous section. Take two readings. Record your data in the table. Then load the balance with two pieces of metal and then three, repeating the measurements as before. Number of Oscillations in 15.0 Seconds Trial Unloaded Balance Balance w/ One Metal Piece Balance w/ Two Metal Pieces Balance w/ Three Metal Pieces 1 2 Average Unit 6: A Property of Matter, Lab A: The Inertial Balance ©2010 by G. Meador – www.inquiryphysics.org 6 A Property of Matter Nam e Lab A: The Inertial Balance Cylinder Version Introduction When you step on a bathroom scale, you measure your weight. Many purchases we make, such as meat and vegetables, are made in terms of weight. Bridges specify the maximum weight they can support. Trucks are rated according to hauling weight limits. When a truck smashes into a building or through a wall or fence, what property of the truck causes the damage? (Speed is not a property of an object, merely a measure of its movement.) In this investigation, we will identify a property of matter which is sometimes confused with weight. The Inertial Balance Clamp the inertial balance to the table with the C clamp as shown in the figure below. Place a protective piece of wood between the balance and the table to prevent scratching. Set the balance in oscillation by pulling it horizontally 10 centimeters to one side. Count the number of complete oscillations (a swing from the starting position, through the resting position, and back to the starting position) occurring in fifteen seconds. (You may need to let the balance lightly strike a piece of paper in order to count the number of swings.) Repeat the exercise once more, and record your data in the table. Next, load the balance with the metal cylinder provided. Repeat the measurements you made in the previous section. Take two readings. Record your data in the table. Load the balance with a 500 gram weight, taping the weight so that it will not shift as the balance oscillates. Repeat the measurements you made in the previous section. Take two readings, and record your data in the table. Number of Oscillations in 15.0 Seconds Trial Unloaded Balance Balance w/ Cylinder Balance w/ 500 g 1 2 Average Unit 6: A Property of Matter, Lab A: The Inertial Balance ©2010 by G. Meador – www.inquiryphysics.org The Idea (FOR EITHER VERSION OF INERTIAL BALANCE ) answer all questions in complete sentences; remember “Affect” is usually a verb while “Effect” is usually a noun 1. W hat is the direction of the acceleration vector of a falling object? 2. W hat is needed to cause an object to accelerate? 3. W hat force causes the acceleration of a falling body? 4. The term that is used for force due to gravity on any object is weight. So the force due to gravity on you is your _________________ . 5. Summarize the results of the lab. (How did the added objects affect the number of oscillations?) 6. W hat is the first explanation you can think of for this data? 7. W hat effect does gravity have on the motion of the inertial balance? Think about the direction of gravity and the direction the balance moved before answering. Explain your answer completely. 8. Given your answer to question 7, what effect does weight then have on the motion of the inertial balance? Explain your answer completely. 9. Your answers to questions 7 and 8 may have invalidated your initial response to question 6. If your answer to question 6 is no longer valid, give the correct explanation below: Unit 6: A Property of Matter, Lab A: The Inertial Balance ©2010 by G. Meador – www.inquiryphysics.org 6 A Property of Matter - Mass Nam e Reading: MASS — NOT A W EIGHTY MATTER You have been investigating the idea of mass. You know that the greater the mass an object has, the greater its tendency to resist motion. Imagine that you push two objects of greatly differing mass – perhaps a large boulder and a small pebble. Because the boulder has a very large mass, it will resist a change in its motion more, and your push will have little effect on it. On the other hand, the pebble can be easily moved by your push. The tendency an object has to resist a change in its motion is called inertia. Inertia has no units, but is directly proportional to (as well as due to) the mass of an object. approximately 4000 miles.) What a marvelous way to lose weight - clearly superior to all the diets you've heard of! But what does it mean to lose weight in space? Does it imply that you've lost your arms or your legs? Don't lose your head - of course not! Weight is the force due to the earth's gravity which acts on you. It changes as you increase or decrease your distance from the center of the earth's gravitational field, which is the geographical center of the earth. But you don't add or lose any matter - your weight changes, but your mass remains the same. When would you become weightless? Now suppose that the boulder and the pebble are coming toward you at 60 miles/hour. Which one would be easier to stop? Since the boulder has greater mass and, therefore, greater inertia, it will be much harder to stop than the pebble. You will have to exert a much greater force to stop the massive boulder. How do we know that your weight in the previous paragraph would be only one quarter of what it was on the earth's surface? This calculation comes from the Law of Universal Gravitation formulated by Sir Isaac Newton. We will study this law later in the course. One of the primary predictions of this law is that the weight of an object decreases as it travels farther from the center of the earth. This is why objects at the equator weigh slightly less than they would at the poles; the earth’s spin makes it bulge around the equator. When a cup sits on a table, there is a pair of forces in balance. Consider the forces acting on the cup. The force due to gravity pulls downward on the cup, but the table counterbalances this force with an equal and upward force. When a car is travelling down a road at a constant speed, a different pair of forces is acting. The forces of air resistance and mechanical friction are being balanced by forces produced by the car's tires. We may conclude from these and similar examples that only unbalanced forces accelerate objects. The mass of an object depends on the quantity of matter in the object, or in other words, on the number and kind of molecules which make up the object. The difference between weight and mass is most apparent when we examine an object in space. If we travel a distance above the earth's surface equal to the radius of the earth, the object will weigh only one quarter of what it weighed at the earth's surface. For example, if you weighed 160 pounds on earth, you would only weigh 40 pounds at an altitude of 4000 miles or 6440 kilometers above the earth. (The earth's radius is Unit 6: A Property of Matter, Reading: Mass – Not a Weighty Matter For hundreds of years after Newton, scientists believed that while weight varied with location in a gravitational field, mass remained constant regardless of location. Are there situations under which mass does change? Albert Einstein suggested that mass was related to energy by the famous equation E=mc2, where c is the velocity of light. Although we have not studied this topic in enough depth to know why, this equation predicts that as an object’s speed increases, its mass increases. This effect only becomes apparent at incredibly high speeds, much faster than we can make large objects move. We can, however, make tiny particles move at speeds near that of light (186,000 miles per second or 300 million meters per second) and his predicted increases in mass do occur. So mass remains constant and unchanging, except when it travels at speeds which are a significant fraction of light speed. ©2010 by G. Meador – www.inquiryphysics.org QUESTIONS answer with several complete sentences 1. W hat is an unbalanced force? W hat does an unbalanced force do to an object? (Be exact.) 2. Victor Vector weighs 650 newtons, while Velma Velocity weighs 750 N. W ho has greater inertia? Describe your entire train of logic which led you to that conclusion. 3. Suppose you were in a weightless environment. If you looked in a mirror, would you appear any thinner? Justify your answer. 4. Under what condition did Einstein say the mass of an object would increase? 5. Describe a situation in which knowing the mass of an object would be preferable to knowing its weight. Be specific and creative! Explain your answer, and be careful not to confuse mass with volume. Unit 6: A Property of Matter, Reading: Mass – Not a Weighty Matter ©2010 by G. Meador – www.inquiryphysics.org 6 A Property of Matter - Mass Nam e W orksheet: The “Vom it Com et” The NASA “Vomit Comet” Zero-Gravity Trainer was used for astronaut training and low-gravity experiments and to film parts of the movie “Apollo 13.” A private corporation later began offering rides on this type of plane for a hefty fee. The trainers are modified jet airplanes. Most of the passenger seats have been removed, and the walls padded to protect the occupants. The planes typically fly for 2 to 3 hours and make 40 parabolic arcs through the air as shown in the figure at right. During each arc, a plane first ascends upward at 45E and presses the occupants down with 2 to 2.5 g’s (19.6 to 24.5 m/s2). Then it traces out a parabola and the occupants feel nearly weightless for 15 to 25 seconds. Then it pulls out with another period of 2 to 2.5 g’s before doing another arc. The occupants are not really weightless - they are simply in freefall. That is, they are actually accelerating toward Earth at 9.8 m/s2 while they both rise and then fall in a plane that is executing a perfect parabola. The gut-wrenching sensations produced on the flights have earned the planes the nickname of the “vomit comets. 1. The plane traces a parabola, so for half of the “weightless” or “zerogravity” period the plane is actually rising through the air, and falling during the other half. Draw the vertical displacement, velocity, and acceleration graphs for the occupants during the “weightless” sensation period, recalling that they are not really weightless, and are both rising and falling. 2. Suppose during one arc the occupants are “weightless” for a total of 20.0 seconds. So they spend 10.0 s ascending and 10.0 s descending. Using the true acceleration of gravity of 9.80 m/s2 , calculate how far the plane would fall in meters and then in feet (1 m = 3.281 ft) from vertical rest during the descending half of its arc: Fall in meters (m): Fall in feet (ft): show your work 3. Let’s suppose that an occupant’s pre-flight weight was 175 pounds. Compute his mass in slugs, using F g = mg where g is 32.2 ft/s2 . Stay in US Customary units throughout your calculation – do NOT convert to SI/metric units. 4. Now convert the occupant’s mass into kilograms, using the US-to-metric mass conversion factor in your notes: Unit 6: A Property of Matter, Worksheet: The “Vomit Comet” ©2010 by G. Meador, www.inquiryphysics.org 6 A Property of Matter - Mass Nam e Lab B: Acceleration vs. Mass Air Track Version How does the mass of an object affect its acceleration? The goal of this experiment will be to find the mathematical relationship between mass and acceleration when a constant unbalanced force is applied. You will again be using an air track and gliders for this experiment. At your lab station are three gliders. The two red gliders each have a mass of 300. g or 0.300 kg. The gold glider has a mass of 150. g or 0.150 kg. The gliders have velcro on their bumpers so that they can be hooked together in certain combinations. In this lab, we will deliberately vary the mass, and observe what happens to acceleration. Mass is thus called the independent variable, and acceleration the dependent variable. W e will hold force (the hanging weight holder), distance, and initial speed constant; indicate those values below: Force Distance Initial Speed 1. Start with all three gliders hooked together for a total mass of 0.750 kg. (Check that you have not hooked the velcro such that a glider drags along the track.) Take three measurements of the time required to constantly accelerate the gliders over a set distance (record that distance below). Record your data in the table. Remember that your times should vary by no more than 0.10 s. 2. Next use just the two red gliders for a mass of 0.600 kg. Repeat step one for this combination. 3. Repeat the procedure for glider(s) massing 0.450 kg, 0.300 kg and 0.150 kg. Mass of Glider(s) (kg) Time (s) Average Time (s) Average Acceleration (m/s 2) 0.750 0.600 0.450 0.300 0.150 Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass ©2010 by G. Meador – www.inquiryphysics.org Calculate the average time and your group's average acceleration for each trial. Use the computer to make a graph from your group's averages. The independent variable should be plotted on the x axis. The dependent variable should be plotted on the y axis. The data will fall into one of the categories at right, and you should have the computer perform the appropriate fit. (Select the “Automatic Curve Fit” function from the “Analyze” menu.) Once you have a good fit, turn off the dot-to-dot line on the graph by de-selecting “Connecting Lines” on the “Graph” menu. Have your teacher approve your graph before printing; save your data. answer in complete sentences 1. W hat happened to the acceleration of the gliders as you increased their mass? 2. Describe the shape of the curve on your graph. W hat kind of function does it represent? 3. That shape/function allows you to predict how mass affects acceleration. If the mass were cut to one-fourth of its previous value, what would the new acceleration be? 4. W rite the full equation for your graph. Remember to substitute the proper variable names for y and x and to indicate the correct values for any constants. Remember to round off values for significant figures. class equation: 5. Let’s test your answer to question 3. Use your graph’s equation to find the theoretical acceleration for 0.100 kg and 0.400 kg of mass. Write down those values and then compare them mathematically in a ratio. (Divide the larger acceleration value by the smaller one.) W rite your ratio down too, using 3 significant figures. Accel. of 0.100 kg = m/s2 Accel. of 0.400 kg = m/s2 Ratio = to 1 6. Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you answer this question. Notice how we changed the mass.) 7. W rite in words the mathematical relationship you have found between mass and acceleration. Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass ©2010 by G. Meador – www.inquiryphysics.org 6 A Property of Matter - Mass Lab B: Acceleration vs. Mass Nam e Air Track Lab Report Version How does the mass of an object affect its acceleration? The goal of this experiment will be to find the relationship between mass and acceleration when a constant unbalanced force is applied. You will again be using air tracks and gliders for this experiment. At your lab station are three gliders. The two red gliders each have a mass of 300 g or 0.300 kg. The gold glider has a mass of 0.150 kg. The gliders can be hooked together in various combinations. Please note that the weight holder has its own mass which must be included in the total mass of the system. You will be writing your own lab report this time. Your lab group must first design an experiment to determine how mass and acceleration are related. Study the equipment available at your lab station. Design your experiment so that you will have data for five different mass values. Be certain that you can answer these questions without notes: 1. W hat are the independent and dependent variables? 2. W hat quantities will you hold constant, at what values, and how will you accomplish that? 3. W hat data must you collect, and what standards of reproducibility will you enforce? (How many trials will you take? How close must the data be before continuing to another trial?) 4. W hat is the best order to the data collection which will minimize human error? Before you take any data, design a data table which is clear and consistent. Use the tables from previous experiments as models. Don't forget that your table needs to have space for calculated quantities as well as raw data. Have one person in the group construct your planned data table on a sheet of notebook paper. After your group has agreed on a procedure and a data table, present your experiment to your teacher for approval. DO N O T C O N TIN U E U N TIL YO U R EXPER IM EN T IS A PPR O VED . Now conduct your experiment. You will need to graph your data and analyze it. The data will fall into one of the categories at right, and you should have the computer perform the appropriate fit. (Select the “Automatic Curve Fit” function from the “Analyze” menu.) • • • • Your lab report must be neatly written or typed; typed reports should be double-spaced Each student will submit a report, with his or her own unique description of the procedure & conclusions Do not use first person in the report (no “I” or “we”, etc.) Past tense is appropriate Y OU R R EPO RT M U ST I N CLU D E THE F O LLO W IN G : Purpose - a statement of the relationship you were exploring (note that you probably did not formulate a hypothesis but merely tested to see what relationship, if any, existed between the variables) Procedure - thoroughly describe what you did, including the equipment used, the set-up, and address the four numbered questions listed above (or a list of procedures written in the imperative mood; be sure the four questions are addressed) Data - your data table (it must be neat; you can use W ord or Excel to create it) and your graph printout Conclusions ! a verbal statement of the relationship you discovered, including the type of curve fit ! an equation that fits the data (substitute proper variable symbols and appropriate rounded values from your best-fit line or curve) ! a discussion of the sources of systematic error in the experiment (see reverse for definition of error types) Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass ©2010 by G. Meador – www.inquiryphysics.org Types of Laboratory Error Type Examples Prevention Discussion personal error (mistakes) mis-reading a scale or incorrectly rearranging an equation or calculating a figure check against lab partners’ work; redo parts of lab as needed when error discovered none; should be corrected before lab is submitted systematic error miscalibration or uncontrolled variables (e.g. friction); includes unavoidable timing errors calibrate equipment when possible; think through procedures to minimize error identify any uncontrollable variables (do not include variables causing random error) random error estimating the last digit on a scale reading; minor variations in temperature or air pressure eliminate when possible; can never be completely eliminated none Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass ©2010 by G. Meador – www.inquiryphysics.org 6 A Property of Matter - Mass Nam e Lab B: Acceleration vs. Mass Dynam ics Cart on Floor Version How does the mass of an object affect its acceleration? The goal of this experiment will be to find the mathematical relationship between mass and acceleration when a constant unbalanced force is applied. In this lab, we will deliberately vary the mass, and observe what happens to acceleration. Mass is thus called the independent variable, and acceleration the dependent variable. W e will hold force (the hanging weight holder), distance, and initial speed constant. You will again be using a dynamics cart, meterstick, and spring for this experiment. Arrange to measure the time required for the cart to accelerate from rest over a distance of 1.00 m, a distance that will be held constant in this experiment. You will use your spring and meterstick to apply a constant force of 2.00 N in this experiment. Start with a cart mass of 6.00 kg as before, taking three measurements of time and recording your data in the table. Then repeat, but lower the mass of the cart to 5.00 kg. Continue the process to fill out the table; calculate the average time and your group's average acceleration for each trial. Mass of Cart (kg) Time (s) Average Time (s) GROUP Average Acceleration (m/s 2) CLASS Average Acceleration (m/s 2) 6.00 5.00 4.00 3.00 2.00 Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass ©2010 by G. Meador – www.inquiryphysics.org Your instructor will indicate if you are to use the computer to make a graph from your group's averages and/or the class averages. The independent variable should be plotted on the x axis. The dependent variable should be plotted on the y axis. The data will fall into one of the categories at right, and you should have the computer perform the appropriate fit. Have your teacher approve your graph before printing; save your data. answer in complete sentences 1. W hat happened to the acceleration of the gliders as you increased their mass? 2. Describe the shape of the curve on your graph. W hat kind of function does it represent? 3. That shape/function allows you to predict how mass affects acceleration. If the mass was cut to one-fourth of its previous value, what would the new acceleration be? 4. W rite the full equation for your graph. Remember to substitute the proper variable names for y and x and to indicate the correct values for any constants. Remember to round off values for significant figures. class equation: 5. Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration for 6.00 kg and 1.50 kg of mass. W rite down those values and then compare them mathematically in a ratio. (Divide the larger acceleration value by the smaller one.) W rite your ratio down too, using 3 significant figures. Accel. of 6.00 kg = m/s2 Accel. of 1.50 kg = m/s2 Ratio = to 1 6. Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you answer this question. Notice how we changed the mass.) 7. W rite in words the mathematical relationship you have found between mass and acceleration. Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass ©2010 by G. Meador – www.inquiryphysics.org 6 A Property of Matter - Mass Nam e Dynam ics Cart and Table Pulley Version Lab B: Acceleration vs. Mass How does the mass of an object affect its acceleration? The goal of this experiment will be to find the mathematical relationship between mass and acceleration when a constant unbalanced force is applied. In this lab, we will deliberately vary the mass, and observe what happens to acceleration. Mass is thus called the independent variable, and acceleration the dependent variable. W e will hold force (the hanging weight holder), distance, and initial speed constant You will again be using a dynamics cart and table pulley for this experiment. Arrange to measure the time required for the cart to accelerate from rest over a large known distance, a distance that will be held constant in this experiment. You will keep the pulling force of the weight hanger constant in this experiment. Start with a cart mass of 6.00 kg as before, taking three measurements of time and recording your data in the table. Then repeat, but lower the mass of the cart to 5.00 kg. Continue the process to fill out the table; calculate the average time and your group's average acceleration for each trial. Fill in the values below for your experiment: Force N Mass of Cart (kg) Distance Time (s) Average Time (s) m Initial Speed GROUP Average Acceleration (m/s 2) m/s CLASS Average Acceleration (m/s 2) 6.00 5.00 4.00 3.00 2.00 Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass ©2010 by G. Meador – www.inquiryphysics.org Your instructor will indicate if you are to use the computer to make a graph from your group's averages and/or the class averages. The independent variable should be plotted on the x axis. The dependent variable should be plotted on the y axis. The data will fall into one of the categories at right, and you should have the computer perform the appropriate fit. Have your teacher approve your graph before printing; save your data.. answer in complete sentences 1. W hat happened to the acceleration of the gliders as you increased their mass? 2. Describe the shape of the curve on your graph. W hat kind of function does it represent? 3. That shape/function allows you to predict how mass affects acceleration. If the mass was cut to one-fourth of its previous value, what would the new acceleration be? 4. W rite the full equation for your graph. Remember to substitute the proper variable names for y and x and to indicate the correct values for any constants. Remember to round off values for significant figures. class equation: 5. Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration for 6.00 kg and 1.50 kg of mass. W rite down those values and then compare them mathematically in a ratio. (Divide the larger acceleration value by the smaller one.) W rite your ratio down too, using 3 significant figures. Accel. of 6.00 kg = m/s2 Accel. of 1.50 kg = m/s2 Ratio = to 1 6. Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you answer this question. Notice how we changed the mass.) 7. W rite in words the mathematical relationship you have found between mass and acceleration. Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass ©2010 by G. Meador – www.inquiryphysics.org Unit 6: A Property of Matter (Mass) Meador’s Inquiry Physics Page 1 of 4 INQUIRY PHYSICS A Modified Learning Cycle Curriculum Unit 6: A Property of Matter (Mass) Sample Notes I recommend that you always write out notes, by hand, on the board for each class. That allows you to control the pacing and focus, rather than having students ignore you while they simply copy down the content of a slide. It also controls your pacing, so that you don’t race ahead but instead focus on student understanding. ©2010 by Granger Meador inquiryphysics.org Unit 6 introduces the concept of mass, relates it to weight, and then develops that mass is inversely proportional to acceleration. Do NOT use “mass” until you get to the discussion phase of 6 Lab A. Ask frequent questions of students to check their grasp of the material, and call upon students to provide the next step when working examples. My rule for students is that if I write it on the board, they must write it in their notes, and I grade their notes each quarter and take off for any units with incomplete notes or examples. Trigonometry-Based Physics (AP Physics B) This unit is identical for both algebra and trigbased courses. Unit 6: A Property of Matter (Mass) Meador’s Inquiry Physics Page 2 of 4 Sample Notes for Unit 6: A Property of Matter Unit 6: A Property of Matter mass (m) = amount of matter comprising an object (think protons, electrons, and neutrons; NOT volume) The notes don’t begin until after the discussion of 6 Lab A. So now the students have begun the process of distinguishing weight and mass. measured in kilograms (kg) or slugs (sl) volume (V) = amount of space occupied by an object measured in liters, cm3, in3, etc. weight (Fg) = force due to gravity on an object measured in newtons (N) or pounds (lbs) density (ρ) = mass/volume measured in kg/m3, sl/ft3, etc. We complete the Example 6-1 table as a signaling exercise where I pose the situation (using a Nerf ball prop), have them think, and all signal simultaneously with a show of fingers how many of the four quantities changed (form an O with fingers if answer is zero). Then we discuss and fill out each row. Example 6-1 Which of these quantities change significantly in each situation? SITUATION object is crushed object taken to the moon object tossed upward half of object is destroyed MASS WEIGHT VOLUME DENSITY no Δ no Δ decreases decreases no Δ decreases no Δ no Δ no Δ no Δ no Δ no Δ decreases decreases decreases no Δ Unit 6: A Property of Matter (Mass) Meador’s Inquiry Physics On Earth, 1 kg weighs 9.8 newtons: 2 9.8 N = (1 kg)(?) insert 9.8 m/s to balance it Page 3 of 4 I put a large newton dial spring scale on the board (using a magnet or hook) and hang a 1 kg mass on it to show them it weighs 9.8 N. so (weight equals mass times the acceleration due to gravity) and the newton is thus equal to a kgm/s2 Conversions 1 pound (lbs) = 4.4482 N 1 kg = 0.068522 slugs weight is not mass, so it is NOT appropriate to convert kg to N or lbs; instead we use Fg = mg Example 6-2 MY WEIGHT AND MASS I use my own weight in example 6-2, asking them to calculate each line with me, but using their own weight. I use a different color marker for all of the numbers that will be different in their own notes. I weigh __170___ pounds. So I weigh My mass is or my mass is “g” is the “acceleration due to gravity” in m/s2 or can be called the “gravitational field strength” in N/kg instead , and it varies with location. I use the PowerPoint in the “acrobat/Other Resources” subdirectory on the CD-ROM to illustrate gravity variations due to location and the effects of special relativity. Example 6-3 GRAVITY VARIATIONS Location g My Weight There Chicago 9.803 m/s2 Fg = mg = (77.2 kg)(9.803 m/s2) = 756.79 N / 4.4482 N/lb = 170. lbs Panama Canal 9.782 m/s2 Fg = mg = (77.2 kg)(9.782 m/s2) = 755.17 N / 4.4482 N/lb = 170. lbs North Pole 9.832 m/s2 Fg = mg = (77.2 kg)(9.832 m/s2) = 759.03 N / 4.4482 N/lb = 171 lbs Space Station 8.71 m/s2 Fg = mg = (77.2 kg)(8.71 m/s2) = 672.41 N / 4.44822 N/lb = 151 lbs Moon surface 1.62 m/s2 Fg = mg = (77.2 kg)(1.62 m/s2) = 125.06 N / 4.44822 N/lb = 28.1 lb Unit 6: A Property of Matter (Mass) Meador’s Inquiry Physics Page 4 of 4 Special Relativity Mass itself varies with speed. Einstein’s Special Theory of Relativity predicts a number of odd changes as an object approaches light speed, and these effects have been experimentally confirmed: mass increases (the inertia of the object increases; it does not have any more electrons, protons, or neutrons but instead they simply become harder to accelerate) objects shrink in the direction of their relative motion time slows down According to this theory where v = speed relative to the observer and c = speed of light = 186,000 miles/second = 3.00x108 m/s Since c is so large relative to v, this effect is only important at immense speeds; even at half the speed of light the mass only increases by 16%. If you want details: Speed 0 Concorde (mach 2; 1354 mph; 605 m/s) Voyager Probe (37240 mph; 16648 m/s) one-half light speed three-quarters light speed 99% of light speed light speed (“warp one” in Star Trek) % of mass increase 0 0.0000000002% 0.000000154% 16% 51% 600% infinite; matter cannot achieve light speed ("warp one") and a similar formula applies to time dilation (time slowing down; confirmed by flying atomic clocks aboard commercial planes and also around Chesapeake Bay; the clocks in the air slowed down just as the theory predicted, falling out of sync with clocks left on the ground) I like to show my students about 8 minutes from a funny 1957 film by Dr. Irwin Moon, The Mystery of Time, which you might be able to to get from http://www.archive.org, but be aware that Dr. Moon had a religious motive and was covering more than special relativity; we only watch 16:42-23:00 of that video. I refer students wanting more details to their textbook and for those who are really motivated, I’ll loan them a copy of Martin Gardner’s excellent book, Relativity Simply Explained (formerly titled Relativity for the Million). Next I show them fun online clips from NASA’s old Vomit Comet zero-g simulator plane and some excerpts on the effects of freefall on the human body from the 1994 video We’re Go for Launch to Zero-G. Then I assign the reading, the worksheet on the Vomit Comet, and we do 6 Lab B. We capture the big idea from 6 Lab B in the Unit 7 notes.