Find Coefficient of Static Friction When Given Angle Object Starts to Slide on Incline

In this problem I placed a box on a board. I then tilted the board to make an incline plane. I recorded the angle at which the box starts to slide. We want to find what the coefficeinet of static friction is for the box and board it is resting on and we want to see if there coefficient of friction changes deprending on surface are of object.
So I took measurements of the angle of the incline when the box starts to move for both the thinnest side being down and the thicker side be down. They are listed in the displayed table. I then took the average of the results.
We will first need to go over how to break down the forces on a incline. Firs there is a the mass times gravity which goes straight down.
Second we have the normal force which goes perpendicular to the surface of the incline plane.
The angle between the mass times gravity and normal force is the angle of the incline.
Now the force making the object move which will be referred to as the force in the x direction connects the normal force and mass times gravity to make a right triangle.
The object will be experiencing a force due to friction loss that will be holding it in place. This is going in the opposite direction of the force in the x direction.
The formula for friction loss is normal force times the coefficient of static friction
Reranging this formula we get firction loss over normal force equals coefficient of static friction
In our experiment we are taking the minimum angle just before the object moves. So this is the angle at which the force in the x direction cancels out the friction loss. So force in x minus friction loss must equal zero.
Reranging this force in x direction must equal the friction loss.
With that knowledge we can now plug in the force in x where the friction loss previously was in the friction loss divided by normal force equals the coefficient of static friction
Inorder to do the next step we will need to know a bit of trigonometry. We are dealing with a right triangle or in other words a triangle with one 90 degree angle. This means that we can use soh cah toa to solve for the normal force leg and the force in x direction leg. So the mass times gravity times the sine of the angle will get the force in x direction. The mass times gravity times the cosine of the angle will get us the value for the normal force leg of the triangle.
After plugging those value in we notice that the mass times gravity gets canceled out.
We then are left with sine of angle over cosine of angle equals the tangent of the angle which equals the coefficient of static friction
With this formula we can solve for the coefficient of static friction.
So the average coefficient of friction between these 2 materials with the thinnest side down is .283. This is completed by taking the tangent of the average experimental angle
Where as the coefficient of static friction with the thicker side down is .279. These values are very close and illustrates that the surface area doesn’t make any difference. As long as the objects rubbing against each other has the same material with same surface finish it will have the same coefficient of static friction. I would also like to add that due to weight not being in the formula it is also not a factor that effects coefficient of static friction.

Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.

[victoriribe]

I am honestly surprised this post has not gotten too much attention yet! I found this video very helpful and the explanation was made very clear with the free body diagram. Keep it going man!

[josuej]

i feel so dumbb after watching this video, my professors make it so hard to understand 😠 THANK YOUUU VERY MUCH FOR THISS!!

[seeyouintea]

I’m doing this in my high school physics class and my teacher had me do a lot more complicated stuff to get the answer. I didn’t know you could just take the tangent of the angle. Thank you

[VAM_Physics_and_Engineering]

For clarification there should also be an equal and opposite normal force which is the incline pushing back on the box. Note normal force is force that is perpendicular to the surface so both the box pushing down and the incline pushing up are normal forces.

[madisonlane]

you’re a lifesaver!! I have a lab like this and I was stuck thank you so much!!

[liangracemalacoco]

i was cramming a physics worksheet of mine. thank you for this video, a life-saver, indeed. :)

[DoiInthanon]

Thank you for the visual demonstration! A very helpful aid for visual learners. Much appreciated!

[jan_direction]

Hey gents. Two years later and this video saved me. Great explanation, really helped a lot. This principle can also be applied to when you need to find the maximum angle before say crutches start to slip right?

[jayasundarrajan]

This was very helpful! Thank you for explaining this in a way that makes sense :)

[josiahlee]

Better teacher than my physics teacher 👍

[TheStickCollector]

I learned about this, but it must have went in one ear and other the other.

I remember it now after watching. Guess i better make it clearer in my notes or something

[geoffcarsten]

so the coefficient of static force is just tan(angle of slip)? ok thanks

[TheSlyFoxThatCreeps]

very good video! helps with my physics test lol

[firstnamelasta]

can i have the name of the app u are using to find the angle? i also need to do this experiment, thank you

[yuvrajkothari]

Hi, if you dont mind, could you please tell me what the surface area's of the boxes were?

[IndesirableShadow]

wow big brain textbook made me confused as heck

[kbim]

its easier to follow when you pause so we cant in take the information.