I am trying to prove that the coefficient of static friction is equal to the tan of the angle of incline. (You can find the proof of this from )
I set the angle of incline as my independent variable and had an angle range from 10 to 37.5 degrees. After setting the slope to different angles, I measured the extra force required to cause the wooden block to begin to move on the slope. I did this by connecting a string to the wooden block and to a container that could be filled with sand (using a pulley to connect them).
μ = (mg sin(θ) + Mg)/(mg cos (θ))
where m is the mass of the wooden block and M is the mass of the handing container and sand.
This simplifies down to μ = tanθ + M/(m cosθ)
However, it is also known that μ = tanθ
Equating the two equations we get tanθ + M/(m cosθ) = tanθ, which is impossible. Can anyone explain what I've down wrong here?
The Attempt at a Solution
I tried manipulating the equation,
M/(m cosθ) = μ - tanθ
=> M = μmcosθ - msinθ
=> M = m(μcosθ - sinθ)
Ultimately, I aim to draw a graph which shows μ = tanθ, however, with the values I obtained so far, no such graph can be drawn.
I would really appreciate it if someone could help me!