Friction Measurement Device

This device allows you to calculate the force of friction between two objects. The concept of it is a platform, that's incline can change by the rotation of a screw, with a surface attached to it (piece of paper, wood...), and an object on it. You turn the screw until the object starts to move, you can measure the angle of the platform, by either using the built in protractor or the cosine. This angle represents Theta critical, which allows you to calculate the force of friction between the objects.

I am a high school student at Toronto French School, and I built this device because I often need to measure the friction between an object and a surface in Physics class, but doing so is awkward, and less precise without a device such as this because I usually resort to a book that I need to hold still as I position the protractor...

This device makes it much easier to measure Theta (θ) critical.

It is entirely designed in Fusion 360 and 3D printed.

• 3D printer(190mm(x)*220mm(y)*180mm(z) minimum)
• Scale(scientific/that measures low values)
• Filament(Approximately 80 grams or less, Ideally multiple colours)
• Surface to test(wood, paper...)(Optional: You can test the surface as 3D printed plastic)
• Object to test
• Ruler(Optional as built in protractor can be used)

• Print one of each, except prime tower, which is optional
• Use supports for the Base(The rails need them)
• Print the screw with care: It is a difficult print because it is tall, so I would suggest using the prime tower I included and a large brim. Also, put travel speed low, retraction high, and z hop to 2mm or more, as well as spacing the screw and the prime tower far apart. This will give the screw time to cool before the nozzle returns to it.
• For less dimensionally accurate 3D printers scale x and y components of screw to 97.5%
• For the screw, I used an MSLA printer, which makes it easier to print.

After having printed all the components, assemble them as shown in the video.

The force of friction is the force between two surfaces in contact that slide against each other. Friction acts in the direction opposite to the direction of motion of the object. This force is crucial in determining efficiency, acceleration and speed of cars as it acts in the direction opposite to motion and therefore must be considered as a force that offsets a portion of the propulsion. It can also be used to calculate how much force is needed to move an object...

To calculate the friction between 2 objects, Theta critical can be used. Theta critical is the angle of a surface at which an object starts to move. This will allow us to calculate the constant of friction, Mu.

For a more in depth understanding, see picture attached.

1. To use the device to measure theta critical, unscrew the screw until the platform is almost flat.
2. Then place the surface you wish to test on the platform.
3. Then the object on the surface.
4. Turn the screw: The object may move because of the oscillation from you turning the screw. This is not Theta critical.
5. Reset object when you get close to Theta critical, and see if it moves.
6. If it doesn't slide, increase slope, and repeat step 5.
7. Once it moves, find the sweet spot by decreasing the slope and testing it again.
8. Once you have decided on a final slope, there are 2 ways to proceed: With built in protractor, or with ruler and formula. Ruler and formula are more precise.

• Method 1: Read the angle of the slope using the protractor. Read using the top of the platform. The first solid line is 10 degrees, and is just above the horizontal line. After that, every solid line is an increase of 10 degrees, and every gap is the 5 degree increment in between. That angle is Theta critical.
• Method 2: Theta critical is equal to arccos((x+43.6)/203) where x is the distance in millimeters between the end of the protractor and the end of the rail(illustration attached) In the other image x is the distance between points H and I.

****You are looking for the angle at which the object starts moving on its own, not more, not less****

This device clearly works, and is very accurate, especially when using the ruler and formula method. To test the accuracy of measurement, I measured the angle in a picture using GeoGebra, which returned about 42.2 degrees. The angle I measured with that setup was 42.9. Very accurate!

After measuring Theta critical of an object on a surface, you need to measure the mass of the object using a scientific scale. This will allow us to determine the force of friction.

****Theta critical is the angle at which the object starts moving on its own, not more, not less****

Using the same formulas as shown previously we can calculate the force of friction between two objects, in Newtons.

Ffriction = Fnormal * Mu

Ffriction = 9.81 * mass * cos(Theta critical) * tan(Theta Critical)

There you have it! Calculating forces may sound complicated, but by using formulas and understanding the concepts it can be made easy enough.