Coefficient of static friction in a 3D Games Engine

[Danilov22]

For a personal project, I am analysing the physics in the Source video game engine and comparing it with real life.

I have set up in the engine a platform which increases in inclination from 0 to around 70 degrees.

On this platform there are four, equally weighted cubes each with a different material property: slime, ice, wood, and rubber. The weights of the cubes are modifiable and the angle of the platform is measurable.

I have been told to use the coefficient of static friction equation. This is listed in "Physics" by Jim Breithaupt (1999, Macmillan Press, ISBN: 0333733028) as:

μ = W sin theta / W cos theta

Is this correct and relevant to my needs? Does this take into consideration the material properties of the blocks? How can I use the results in a meaningful manner?

Additional:
I have been told that this experiment can be used with the equations:
sin theta * gravity * mass = pulling along force
cos theta * gravity * mass = pulling down onto surface force

Any explanation into this would be greatly appreciated,
Kind regards,
Danilo Vujevic.

 

[LostConjugate]

All that is saying is that 100% of the gravitational force is pulling against the surface when there is no angle. cos(0) = 1

If the angle is 90 degrees, cos(90) = 0, 0% of the gravitational force is pulling against the surface.

cos(45) = 1/2, so at a 45 degree angle half of the gravitational force is working to move the object along the board, and the other half is working to increase the friction.

So as you increase the angle you increase the force (and decrease the friction), the lower the static friction coefficient the sooner the object will break free of it's standing position.

(mg)cos(theta) < C * (mg)sin(theta) while the object is not moving.

Where C is the coefficient you are looking for. I think that's right.

 

[PhanthomJay]

μ = W sin theta / W cos theta

Is this correct and relevant to my needs? Does this take into consideration the material properties of the blocks? How can I use the results in a meaningful manner?

It is correct for a non accelerating incline, and since the W cancels out, u_s =sin theta/cos theta, which further simplifies to u_s = tan theta. Theta is the angle of the incline with respect to the horizontal. As the incline is slowly raised, the block will just start to slip at a certain angle. Record that angle, and calculate u_s as the tangent of that angle. As noted above, the material with the higher coeficient of static friction will slip at a greater angle.

Additional:
I have been told that this experiment can be used with the equations:
sin theta * gravity * mass = pulling along force
cos theta * gravity * mass = pulling down onto surface force

Any explanation into this would be greatly appreciated,
Kind regards,
Danilo Vujevic.

These equations are just part of the solution..Newton's first law provides the other equations which lead to u_s =tan theta.

 

[Danilov22]

Firstly, thanks a lot for the rapid responses!
So for my experiment where the incline slowly increases linearly, I should just record the angle at when the different types of blocks begin to slide?
For example, the ice block begins to slide at 5 degrees.

u_s = tan theta
u_s = tan 5
u_s = 0.087

Therefore the coefficient of static friction for ice in the game engine is 0.087. Is this correct?

 

[PhanthomJay]

Yes, be sure to raise the ramp slowly and smoothly, and repeat the experiment several times to get an average value of the angle when they just start to slide (don't overshoot the angle). You should probably round off the answer to 2 decimal points, depending on the accuracy of your measurement of the angle.

 

[LostConjugate]

Record that angle, and calculate u_s as the tangent of that angle. .

Isn't it the cotangent of the angle of incline? See my equation above.