Rubber Band Car Physics Project

This is a work in progress. I am adding things as this unit progresses...

Project Goal: to do some real physics -- specifically, to get experience applying rotational motion, and energy concepts in the context of rubber band cars.

Contest Goals: 1) to design a rubber band car that will reach the fastest possible top speed and 2) to predict that top speed without actually allowing the car to accelerate.

Phase 1: learn basic rotational motion concepts and apply those concepts to the process of analyzing a basic car. Measure wheel and axle moments of inertia, car mass, and motor output, and use those data to calculate maximum speed. Experiment with various motor designs and ponder how you might be able to give your car more energy -- and what the tradeoffs might be.

Phase 2: design your own car that will go as fast as possible, within the constraints of the project. The primary variables to consider are frame length, wheel diameter, and overall mass, but youcan also perform some other "outside the box" modifications to try to make your car go faster.

Phase 3: assemble and analyze your new car, without actually letting it accelerate. Collect data and perform calculations to predict your car's top speed (essentially a repeat of phase one, but with your car). When you're done, submit your prediction to the judge.

In Phase 4, Now you can actually accelerate your car. You can also modify it in order to get its performance to match your prediction.

Contest Day: Get your car's top speed (at a "finish line" that you specify) measured by the judge. The team with a combination of highest speed and best prediction (according to the scoring formula) wins.

These are the parts for a basic, 12" frame car.

Refer to the parts diagrams. Here are the parts you'll need -- and how many of each.

Screws: Just about all of the screws are 1/2" #6 screws. The exceptions to this rule are...

1. If your wheel hub set screws (to tighten the wheel hub to the axle) strip out their holes, try replacing them with #8 screws.
2. The adjustment screws on the steering adjustors should be 5/8" or 3/4" long #6 screws.

Frame Parts:

1. 2 Frame Side Pieces
2. 2 Frame End Caps (one with a center hole, one plain)
3. 3 Frame Crosspieces
4. 10 Frame Lock Tabs
5. 4 Skateboard Bearings
6. 4 Bearing Hubs

Axle and Wheel Parts:

1. 2 Axles
2. 4 Wheel Hubs
3. 4 Spacers
4. 2 Large wheels
5. 2 small wheels
6. 4 slices of bike tire tube (about 1.5" wide) -- for traction
7. Extra-wide rubber bands for better traction

Rubber Band "Motor" Parts:

1. 1 Rubber band (or more if you want to try)
2. 1 Rubber band stopper
3. 1 Rubber band harness
4. 1 Release pin harness
5. Fishing line (1 foot or less)

Watch the video. This is the short version. I have a longer version, but I don't think anyone will watch it at this point. Maybe I will add it later.

Choose your Parts Configuration: Select a frame length between 9.6" and 23.5". Select pairs of wheels with diameters between 2" and 11". For your frame, select centered braces or offset braces. Also select the "spacious drive axle" design or the standard design (with less space around the drive axle).

Considerations:

1. Traction and Wheel Force:
2. The force your car can use for acceleration is limited by the force of static friction between the drive wheels and the floor. This force of static friction is limited mostly by the coefficient of friction between your drive wheels' surface and the floor's surface and the normal force between your drive wheels and the floor. The normal force is essentially the weight with which those wheels press against the floor. If your wheel force exceeds the force of static friction, the wheels will slip, causing the car to waste energy and likely veer out of control.
3. Energy
4. The car gets its energy from work done by the rubber bands. Work = Force x Distance. Your car will go fastest if the product of force and distance is as high as possible. But too much force causes the wheels to slip. And regarding distance, there is only so much space in which to stretch the bands. Plus, if you stretch the bands too far, the force can become too high.
5. Mass
6. Mass has inertia, and inertia is resistance to acceleration. Given the same force, a smaller mass will accelerate faster. But all of the car parts that provide force and make a car go fast have mass.

Get a copy of the Rubber Band Project Data and Calculations spreadsheet, and share it with your group members. Enter all of your project data and calculations in the spreadsheet.

1. Assemble your car.
2. Get a string with a loop on each end. The entire length should be around 70-80cm (so the falling weight almost reaches the floor -- see later steps).
3. Attach one end of the string to your drive axle. Do this by pushing one of the loops through the axle hole and then passing the other end of the string through the loop. Tighten.
4. Lube your bearings (unless you've already done it). Holding your car sideways, drip a drop or two of WD-40 in one bearing. Spin the axle to wind the string a little. Pull the end of the string to spin the axle rapidly back and forth, working the lube into the bearing. Repeat with the bearing on the other side of the axle.
5. Find a weight to accelerate your wheels and axle. For 4" wheels, a 100g weight works well. For larger wheels you should probably use more weight. Record the mass of the falling weight.
6. Attach the weight to the other end of the string.
7. Wind up the string until the loop knot touches the axle. Don't let the string wind on top of itself any more than you have to.
8. Prepare to let the weight fall. You will need to do two things...
9. Record a slow motion video of the weight falling. [If you are using an iPhone, you should do a shut down and restart, or it might not actually record at 240fps.] This is the "fall time."
10. Stop the weight when it rises back up to its highest point. While you're holding it here, measure and record the distance from the knot by the weight to the axle. This is the "distance risen."
11. Now just let the weight go to its lowest point and stay there. Measure and record the distance from the knot by the weight to the axle. This is the "descent distance."
12. Now count the number of wheel and axle rotations required to wind the weight back up to its starting point (with the knot at the axle). Make sure that you're winding the same way that you wound before. This is the angular displacement, in rotations.
13. Make a copy of the attached spreadsheet. Enter your calculations. Do not enter units in the data cells. I recommend doing your scratch work on paper and entering formulas directly into the spreadsheet.

1. Remove your other wheels and axle from the car.
2. Calculate one wheel's moment of inertia
3. Measure the wheel radius.
4. Measure the total wheel mass. [If we were going to be very precise, we would remove the hub and screws and calculate their MOI separately, but leaving them on will give us an adequate estimate.]
5. Calculate the moment of inertia of one wheel using the formula for MOI of a disk: 1/2*m*r^2.
6. Calculate the axle's moment of inertia
7. Measure the axle mass
8. You do not need to measure axle radius. It is provided. These axles all have radii of approximately 0.004m.
9. Calculate the moment of inertia of the axle using the formula for MOI of a disk: 1/2*m*r^2. It can be thought of as a very thick disk.
10. Calculate the total moment of inertia of the wheel and axle by adding the individual moments of inertia of two wheels and the axle. You may assume that the two wheels have the same MOI.

Design a motor with some type of rubber band configuration. Wind up your car and do some "false starts." You can't let it get up to full speed, but should let it start accelerating. If the wheels slip, wind the car up less. If they don't slip, wind it up more. The more you can wind it without slipping, the faster it will go. Once you've determined how far you can wind it, find a way make sure that you can repeat this exact winding (for example, you might want to make a mark on your string, at the point where it touches the axle at maximum winding).

In this step, you will determine how much energy your motor is producing by finding out how much it can accelerate your drive wheels and axle. In the contest, this energy output will be distributed between translational KE for the entire mass, and rotational KE of both wheels and axles. This is also a good time to measure your car's acceleration distance.

Part 1: Counting the rotations to wind-up the motor

1. Stick a piece of blue tape to the outside of one of the drive wheels, pointing from the axle outward.
2. Count the rotations of your drive wheels and axle by looking at the blue tape as you wind up your motor to its maximum (the maximum winding without causing "spinout"). Record the number of rotations during winding.

Part 2: Use the motor to spin your drive wheels & axle, and measure their kinetic energy -- this provides a measure of your motor output energy. There are two methods:

Method 1: -- Slow Motion Video (see first video, above)

1. Create a slow-motion video meeting these requirements. [iPhone users perform a restart first.]
2. The video should show the drive wheel and axle spinning just before and after it reaches its maximum speed.
3. The blue tape that you added to a wheel should be clearly visible.
4. There should be an indication of when the wheel has reached top speed. For example, if you have a release pin, your video should show the release pin. When the pin releases, you know that the wheel and axle has reached top speed.
5. Trim the video so that it is as short as possible (while still capturing everything above). Make sure that the entire segment is in slow motion.
6. Record your frame rate (probably 240fps)
7. Right there on you phone, open the Vernier Video Analysis app. The link is in Google Classroom.
8. In the app, use the slider to advance to the part of the video where the wheel and axle has reached maximum speed.
9. Use the video frame counter (bottom left) and the frame-by-frame advance button to determine how many frames elapse as your wheel makes one rotation. Record the number of frames. If it's not an integer, you can estimate fractions of a frame. Or you can go through another rotation. The data sheet defaults to 1 rotation, but you can change that.
10. Using the frame rate and the number of frames per rotation, you can calculate angular velocity, in rad/s.

Method 2: Photogates (see 2nd video, above)

1. Use some masking tape to create a little "flag" that extends from the edge of one of your car's drive wheels (see "method 2" video).
2. Open the Vernier Graphical Analysis App (link in Google Classroom)
3. Connect a labquest mini to your Chromebook, and connect a photogate to the labquest.
4. Follow the steps to connect your photogate sensor.
5. Click on the "photogate timing mode" button in the bottom left, and enter the settings in the attached figure. By setting the "flag spacing" to 6.2831m, we're employing a workaround. Every time the wheel's flag passes through the gates, the sensor will think the wheel has traveled 6.28m. If it does this every second, the velocity graph will read 6.28 m/s. But it will really be 6.28 radians/second! :-)
6. Wind up your car, start collecting, position the photogate sensor just off the wheel edge, and let it rip!
7. Make sure the graph is showing velocity, and then look for the maximum. That's the angular velocity that you will need to

Part 3: Wrapping up and calculating Max KE

1. Look up and record your Drive Wheels and Axle MOI that you found in a previous step. You will need it here.
2. Also look up and record your drive wheel radius.
3. Calculate max KE. For a wheel rotating in place, KE = 0.5Iw^2. The max rotational KE for this test is your motor output.
4. Use the number of winding rotations and your drive wheel radius to calculate the acceleration distance. When your car accelerates, the drive wheels will turn just as many times as they did as you were winding up the car -- only in the opposite direction. If you know their radius (which you do), you can calculate the distance the car will travel.

1. Use a force meter, a scale, or multiple spring scales to measure your maximum band force. Measure this in Newtons.
2. Look up your drive wheel radius from an earlier step.
3. To find the maximum torque you will need the correct radius when your car is fully wound. When your car is fully wound, are the bands still acting on the axle at the same radius, or is the axle thickened by layers of string and rubber band? Estimate and record the radius at which the bands are applying their force. Remember that the bare axle is around 0.004m. If your bands are piled up, the effective radius should be bigger.
4. The "Motive Force" is what I am calling the force of friction that the floor uses to push the car forward. It is the same as the backward force of friction that the edge of the wheel applies to the floor. You can calculate this if you know the torque and the wheel radius.

Measure and record your car's overall mass. If you have completed the other steps, you have already collected all of the other data that you need. On the spreadsheet, gather up the requested data. Then perform your calculations. The recommended problem-solving strategy is to set your car's motor output energy equal to your car's three kinetic energies (Overall translational KE, and a Rotational KE for for each set of wheels and axle). Convert angular velocities to linear velocity, and solve for v.

When you're done, enter your calculation. Then decide if you really believe it. If you don't, you can guess any maximum speed that you want. Enter it in the turquoise cell. Your contest score depends on that guess.

This is the end of the "Group Test" part of the project. Submit your spreadsheet for grading.

DO NOT MOVE ON TO THIS STEP UNTIL YOU HAVE OFFICIALLY SUBMITTED YOUR MAX SPEED PREDICTION.

1. Establish a location for launching your car. Make sure that the car will be in a well-lit area when it reaches its maximum speed.
2. Record a slow motion video of your car reaching its maximum velocity. If you can see the axle pin release, that is a good indicator that your car has reached its top speed.
3. Choose one or more floor tiles over which to measure your car's top speed. If you know the car's acceleration distance, you can mark these tiles with blue tape before you make your video.
4. Use your video to determine your car's transit time across the "finish line."
5. Method 1: Use The Vernier Video Analysis App.
6. Trim your video so that it is a small as possible, but make sure that it is all slow motion and that it includes the interval when it traverses the floor tiles you have chosen. Save this small version of your video.
7. Open the video in Vernier Video Analysis. You should be able to do this efficiently on a phone, but you can also upload the video to your Google Drive and then download it to your Chromebook.
8. Select the icon that looks like a table to deselect the graph, so that the video is bigger.
9. Record the frame number at which a part of the car crosses into the floor tiles that you have chosen for your maximum velocity measurement interval.
10. Record the frame number at which that same part of the car leaves the floor tiles that you have chosen.
11. Use the number of elapsed frame numbers and the frame rate of the video to determine the time to cross those tiles.
12. Method 2 (for iPhones):
13. Open the video in your photos app. In the photo app, the video time seems to be very reliable in editing mode, but not in viewing mode, so get into editing mode...
14. Click the edit button
15. "Scrub" along with the slider until a part of the car reaches the beginning of the interval that you have marked (or a floor tile edge that you want to use as the beginning of your finish interval. When your finger is on the slider, the time should display. Record this time -- the moment a part of the car reaches the finish interval.
16. Keep moving the slider until the same part of your car reaches the end of the finish interval.
17. Subtract initial time from final time to find the change in time.
18. Calculate speed = distance/ change in time, where the distance is the distance across the foot-long tiles, converted to meters.

The frames are made of MDF fiberboard. It is nominally 1/8", but I laser cut the slots to 0.101". If you need to scale any of the attached files, scale the slot widths to 0.101 inches. Everything is in inches, which may be troublesome with the .stl files, since people (and 3D printers) are accustomed to those being in millimeters.

Here is a link to a Google Drive Folder with IGS, STP, and 3DM files. I couldn't attach them below.

I didn't want to provide this much help at first, because I wanted everyone to have the experience of attempting the problems on their own. I am making it available now so that it is here for you when you begin working on your corrections. It is also here for students who are struggling with their initial calculations, check their email, and are willing to watch some of these videos in order to do the calculations correctly the first time.

**The data set that I used for these calculations is provided below -- but without the formulas :-(

If you want to see if you're doing the calculations correctly, here are some practice data sets with corresponding answers. I intentionally did not include the formulas.

1. Practice Data Set 0 -- these are the data that I used in the videos above, in case you want to do any of those calculations "with me."
2. Practice Data Set 1
3. Practice Data Set 2

**If you think I got anything wrong, please let me know so that I can take a look and maybe fix it. I've been known to make mistakes on my answer keys.