

Subject:
Science Project for 3rd grader
Category: Science > Physics Asked by: 4448donga List Price: $5.00 
Posted:
02 Apr 2006 11:36 PDT
Expires: 02 May 2006 11:36 PDT Question ID: 714659 
My 3rd grader and I have completed most of her science fair project. The project involved building two identical vehicles out of styrofoam. The vehicles are exactly alike EXCEPT for the size of the wheels. We have been able to complete the entire project except for background knowledge/research. We have determined through a series of "races" that the vehicle with the smaller wheels goes faster down the inclined plane. After spending several hours on the internet, I have been unable to find out WHY the smaller wheels go faster. I found one reference to it on a message board, but the terminology was way beyond her comprehension  and mine! Please help!! WHY DO SMALLER WHEELS GO FASTER THAN LARGER WHEELS??  


Subject:
Re: Science Project for 3rd grader
Answered By: hedgiega on 04 Apr 2006 01:14 PDT 
Hi Don, Nice experiment! In this explanation, I will try to give you both the physics and pointers to a way to help your daughter understand it. You have several factors present in your experiment: 1) total mass of the two vehicles (You should weigh both, to determine their mass) I expect the one with bigger wheels will be a bit heavier  so you have masses m.A and m.B and slightly different inital energies (E= m * g * h) with (m = m.A or m=m.B) 2) Friction  The bigger wheels result in smaller rolling friction (This is why bicycles are made with bigger wheels.) These two factors would favor the conclusion that vehicle B (=Bigger wheels) will be faster, the opposite of what you found. That leaves the third factor to explain your data: 3) Inertia: a) linear inertia of the vehicle and b) rotational inertia of the wheels Inertia opposes acceleration and does in two ways a) vehicle B (with total mass m.B) has harder time picking up speed (this cancels advantage 1) b) the vehicle with wheels which have larger inertia has harder time getting them rolling. http://commons.bcit.ca/physics/demos1103/DLD/DLD19.htm It is more difficult  takes more energy  to get larger wheels rolling; they have a harder time picking up speed. If your daughter has a bicycle, you could call her attention to the force she has to exert to get it started (overcoming inertia and friction) vs to keep it going (overcoming frictio only) vs going up the hill (overcoming friction and gravity) ____________________________ I disagree with the comment by qed100ga on 02 Apr 2006 13:21 PDT that to do experiment is sufficient. It's great that you want to understand the result. I suggest you do additional observations to verify understanding of your results: a) You may estimate the kinetic energy of the vehicle at the bottom of the ramp. To do that, terminate the ramp with a gentle curve (to avoid impact with the table) and observe how far and how quickly vehicles A and B run on the table after they leave the ramp. this is a picture of 'gentle termination' of a ramp http://www.andamooka.org/newtphys/figs/bk1/ch03/ramp.JPG taken from here: http://www.andamooka.org/reader.pl?pgid=newtphysbk1ch03 Kinetic energy of vehicles will be stored in forward movement of the whole vehicle (forward speed v) and in the rotation of the wheels (angular velocity or RPM) If factor #3 is significant, vehicle B will run further before it stops. You still have two factors here less friction, and possible larger inertia. So  how can you separate them? b) Attach weights I) to the body II) to the wheels (In two ways, close to and farther from the axis) that will affect factors #1) and #3) differently and will not change factor #2) the friction too much. Make an estimate/guess of the effect of weights and see if the additional experiments confirm your understanding and data. Have fun, and do not hesitate to post an RFC (and/or results) __________________________________________ Few links for the background and formulas: The effect 'rotational inertia sucking away energy' is actually a physics FAQ best illustrated by: "For a final activity take a ring and a solid disk [same mass] and roll them down a ramp..." http://www.iit.edu/~smile/ph9117.html http://csats.psu.edu/files/GREATT/Flywheels/Flywheels.htm Simple explanation is here: (moment of inertia = rotational inertia , which resists change in angular velocity) The more mass is distributed farther from the axis, the greater the moment of inertia. And the greater the moment of inertia, the more resistance to changes in rotational motion. So as objects roll down the ramp, potential energy is transformed into translational and rotational kinetic energies, but the object with the greatest moment of inertia rotates more slowly. http://acad.udallas.edu/physics/GP1/rotational_motion_ii_faqs.htm SEARCH TERMS: rotational inertia ramp brings more info on Moment of Inertia (of full and hollow cylinder) http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.inertia.html http://physics.ucsd.edu/students/courses/summer2002/ss1/physics2bl/EXPER2_overview.htm also SEARCH TERMS: rolling friction ramp such as: http://teacher.scholastic.com/dirt/roll.htm Do not miss: http://images.google.com/images?client=opera&rls=en&q=rolling%20friction%20ramp Picture at www.andamooka.org (used above) shows a 'gentle ramp termination' and leads to some 'Balls and Ramps Study' of other researchers http://www.belmont.k12.ma.us/winnbrook/index.html?class_pages/first.htm If you find a way to change the shape of your ramp, you can ask which shape will bring the ball down fastest  and (re) discover the Brachistochrone curve http://en.wikipedia.org/wiki/Brachistochrone http://www.du.edu/~etuttle/math/brach.htm http://images.google.com/images?q=Brachistochrone This sets of slides Rolling Cylinders Demonstration (This may be too advanced, but the pictures may be of interest) "..involves different cylinders rolling down a slope Depending on their moment of inertia, they accelerate at different rates. Download a PowerPoint presentation explaining the experiment..." http://www.physics.gla.ac.uk/misc/teachers/index.html#rollingCylinders 

Subject:
Re: Science Project for 3rd grader
From: pinkfreudga on 02 Apr 2006 11:46 PDT 
This article may provide a bit of insight. It's not written at the third grade level, however: http://heawww.harvard.edu/~fine/opinions/wheelsize.html 
Subject:
Re: Science Project for 3rd grader
From: rainbowga on 02 Apr 2006 11:48 PDT 
Not sure if this is the forum you found, but it may help: http://www.physicsforums.com/archive/index.php/t3071.html Rainbow~ 
Subject:
Re: Science Project for 3rd grader
From: qed100ga on 02 Apr 2006 13:21 PDT 
Here's something which may give you a lift. Consider this: You have performed an experiment. You've controlled all the relevant variables. You kept all the variables constant except one, the wheel radius, and you've faithfully collected data on speed vs wheel radius. You notice that, all other things kept equal (including the energy source), the speed of the car is related statistically to the wheel radius. But you don't know at this point exactly *what* the deep connection is between speed & radius. Does this mean that you and your daughter have failed the science project? Not at all! :) The backbone of scientific exploration, before theory, is experiment. And in experiment, there is no promise, no pretense, of arriving at a deep theory to connect & explain all the data. As long as your experiment has been done rigorously and honestly, then you can also honestly be said to have done a good work of science. ...Now of course you still *want* to know a good theory of the contribution of wheel size to speed. You are prodded to ask for such a theory by the conspicuous correlation in your data. It's something to aspire toward. But, the question always comes before the answer, and there's no guarantee of having the answer. Many questions in science persist in going unanswered, even after decades, or even centuries, of research. So to reiterate, if you've done the experiment, then you've done as much science as can be expected of anyone. You can look for some source of insight into this question (and if you're really curious, you will). But even without that answer your child can write up a perfectly legitimate summary of the methods & results of her research, and could be deserving of a high grade for her work. Be proud. 
Subject:
Re: Science Project for 3rd grader
From: rracecarrga on 03 Apr 2006 14:34 PDT 
Here is the key pointthere are 2 different things that move down the inclined plane: 1) the wheels 2) the body of the car. Both start from a standstill, and gravity pulls on them, gradually speeding them up down the plane. BUT there is a difference between the two. The body just has to move down the plane, while the wheels have to move down the plane AND start to spin. So it's harder for the wheels to speed up than it is for the body. Assuming you have no significant friction in your bearings, if you just take a wheel of one of the cars and roll it down the ramp by itself, you will find that it goes slower than either one of the cars. It has a speed it 'wants' to go (this speed is the same for a big wheel and a little wheel). The body 'wants' to go faster, and if you could somehow get rid of friction, the cars would slide down at this faster speed. So, wheels tend to slow down the bodies, and the bigger wheels, being a bigger fraction of the total mass of the vehicle, are able to 'get their way' more, and so the car with the big wheels goes slower. Bottom line: the fact that wheels have to spin as well as move down the plane slows them down. 
Subject:
Re: Science Project for 3rd grader
From: marcuslga on 03 Apr 2006 17:22 PDT 
It's a concept of "Work", not exactly 3rd grader material but not too bad. Gravity is doing all the work on your box rolling down an incline. for all purposes, we ignore everything else. the work gravity has done from top to bottom is the same whether you have small wheels or big wheels, neglecting mass difference. that equation is mass * gravitational acceleration constant * vertical height, or mgh. this will be the same for value for both cars. that term is equal to the kinetic engergy at the end, which, without wheels, or with very very small wheels, would be 1/2 * m * velocity^2. but with wheels, the mgh term is equal to 1/2 *m * velocity^2 plus a new term accounting for the work done rotating the wheels themselves. that term is 1/2 * I * angular velocity^2. the higher this 1/2Iw^2 term is , the lower the 1/2mv^2 has to be, so the lower your velocity down the track. the I is "second moment of inertia", which is 1/2 * mass of wheel * radius^2. I have no idea what kind of math skills a 3rd grader has so this is likely worthless info. If you wanna explain it to a 3rd grader, I'd say... Take a full soup can. Spin it around in your hand. Notice it takes effort to spin it. A larger can will be harder to spin. That's like your wheels. Gravity will give your carts the same amount of energy regardless of the wheel size. But the more energy that's used to spin those wheels, the less that's available to move the actual cart down the hill. Initial potential energy = Final kinetic energy 
Subject:
Re: Science Project for 3rd grader
From: grevesga on 03 Apr 2006 23:20 PDT 
Greetings, This problem has to do with a measure of the wheel called the "moment of inertia." Before I explain what this term represents, it is a good idea to review basic kinematic concepts. Typically, in basic physics problems like this, we start off by dealing with what is called "linear motion," that is, things which move in a straight line. These things can obviously have a position, speed, acceleration, and so on. One other thing they have is a mass. In linear motion problems (this problem of a car, specifically a wheel, is NOT a linear problem  more on that in a moment) there is also a mass which acts at the "center of mass" of the object in question. Let me just clarify that for a moment. If you think of a basketball, it has some weight, maybe a quarter pound or half a pound. This basketball is also quite large, but in physics the size is not a problem. The problems treats the basketball as if all of its mass were concentrated at the center of the ball. This is called the center of mass. http://en.wikipedia.org/wiki/Center_of_mass In rotational motion (a wheel rotates, like I said before it is not linear) there is something sort of like mass. However, this quantity has to do with how the mass of your object is arranged around its center of mass. This is the moment of inertia that I was talking about a moment ago. http://en.wikipedia.org/wiki/Moment_of_inertia http://hyperphysics.phyastr.gsu.edu/HBASE/mi.html In a basketball, all of the mass is on the outside, since inside there is nothing but air (very low mass). Thus, the moment of inertia will be different than a big red dodgeball which weighs the same, but who's mass is on the inside as well as the outside. There is another important concept to introduce before the solution to your probelm will be apparent: kinetic energy. Specifically, there are two types of kinetic energy we want to consider: that due to the linear motion, and that due to the rotating motion of the wheels. The linear kinetic energy depends on two things: mass and speed of an object. Similarly, the rotational kinetic energy depends on two things: moment of inertia and ROTATIONAL speed of an object (think RPM  revolutions per minute). More on kinetic energy and rotational kinetic energy here: http://theory.uwinnipeg.ca/mod_tech/node50.html Now, there is one last concept called work to deal with. Fortunately, work is just a fancy name for "change in kinetic energy." The "WorkEnergy Theorem" says precisely that  Work is equal to the change in kinetic energy. In this problem, the only work done on your wheel is the work done by gravity. The car starts at the top of the hill at rest. At the bottom it is moving. The motion is due to gravity, hence the work is done by gravity. Now, if both of your cars weight the same amount, then this work will be the same amount (see this link for the equations: http://hyperphysics.phyastr.gsu.edu/HBASE/gpot.html ). Since the motion at the top (when you start the car on the ramp) is nothing, there is no kinetic energy. Since the work is the same, the cars must have the same kinetic energy at the bottom of the hill. Remember, kinetic energy is broken into two parts: kinetic energy = rotational + linear Now, remember that rotational kinetic energy depends on the moment of inertia, and the moment of inertia in turn depends on two things: moment of inertia = mass x distance (from the center of mass of the object) So, what happens if you make the distance smaller (i.e. smaller wheel)? Smaller wheel > smaller moment of inertia > smaller rotational kinetic energy. But if the rotational kinetic energy is smaller for the small wheel than the big wheel, but the TOTAL kinetic energy is the same, we have the following situation: TOTAL energy (small wheel) = TOTAL energy (big wheel) rotational (small wheel) + linear (small wheel) = rotational (big wheel) + linear (big wheel) But rotational (small wheel) is less than rotational (big wheel). This means that linear (small wheel) is BIGGER than linear (big wheel). If the LINEAR kinetic energy is bigger, we must go back to the formula for linear kinetic energy: kinetic energy depends on mass and speed. If the mass stays the same, and overall the amount must increase, only one thing is left to do  increase the speed. I hope this wasn't too technical an argument, I will summarize it below:  (Legend: K = Kinetic energy, I = moment of Inertia, M = Mass, D = Distance, S = Speed, R = Rotations per minute (RPM), ~ = "depends on") K ~ rotational K, linear K rotational K ~ I, R linear K ~ M, S Now, I ~ M, D For a small wheel, obviously D is smaller, thus I(big) is larger than I(small). This implies that rotational K(big) is larger than rotational K(small). Since final K(big) is exactly the same as final K(small), we know that linear K(big) is SMALLER than linear K(small). But now linear K(small) ~ M, S. M does not change, so the only thing left to change is S, the speed of the smaller wheel, and it must become larger than the speed of the bigger wheel.  If you want to do the calculations, all you would need is a standard calculator and the equations, which can be found on any introductory physics website, such as: Example problems http://www.dac.neu.edu/physics/a.cromer/Physics1192/Dynamics.html Common moments of inertia http://kosmoi.com/Science/Physics/Mechanics/tpecp21.gif Equations / lecture notes http://www.colorado.edu/physics/phys2010/phys2010_sm99/NOTES/Lecture13.html If you can provide all of the measurements necessary (radius of the wheels, type of wheel i.e. solid or just a hoop, mass of wheel, mass of car, angle of ramp, height of ramp) I would be happy to walk you through the calculation, it is not too complicated once you have the numbers. 
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