Finding the coefficient of friction, ramps and acceleration

[gRACK]

Homework Statement

mg sin θ/mg cos θ = μ (coefficient of friction)

sinθ/cosθ = tanθ

The Attempt at a Solution

then does μ = tanθ/mg (which is what my teacher said, although I'm not sure i understand) OR is the above equation simplified so that μ = tanθ?

thanks for your help - and any other information on finding the frictional force, acceleration etc. would be good too. I read that the coefficient of friction is always a constant. but is this still true if the acceleration increases? i should make things clearer: i have some data from an experiment where a trolley is released from the top of a ramp, but the height is altered each time. (there's also a light gate involved too, but I'm not stuck on that yet - although any passing info would definitely be useful, thanks)edit: also, I plotted an acceleration v. sinθ (the angle of the ramp) graph, and expected that the gradient would be 9.81 , and that the intercept would either be 0, or below (due to frictional forces). instead, the intercept was actually a bit above 0 and the gradient wasn't 9.81 (but close). Should i bother trying to explain this..as i don't really know how to, or is just some discrepancy when i plotted the graph using excel?

 

[Kurdt]

The situation is complicated because there are two types of friction. Static and kinetic. From what you describe, this sounds like kinetic friction. SO your first equation won't really apply, as that is balancing the object with the force of static friction.

Coefficient of friction is approximately constant for a range of speeds. See the following page.

http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html

I take it you're measuring the acceleration of the trolley down the ramp and varying the angle. What you want to do is work out how the two are related again. Remember the coefficient of static fiction with be approximately constant as the trolley moves down the ramp.

 

[Moetasim]

First, let's clarify the equation for finding the coefficient of friction. The correct equation is μ = tanθ, where θ is the angle of the ramp and μ is the coefficient of friction. This equation is derived from the fact that the frictional force is equal to the normal force (mg cosθ) multiplied by the coefficient of friction (μ). So, mg sinθ/mg cosθ = μ, which simplifies to μ = tanθ.

Now, to address your question about the coefficient of friction being a constant. The coefficient of friction is a constant for a given pair of surfaces. However, it can vary if the surfaces change or if the conditions change (e.g. temperature, humidity, etc.). In your experiment, the coefficient of friction may change if the surface of the ramp or the trolley changes. Additionally, if the acceleration increases, the coefficient of friction may also change due to the increased force between the surfaces.

As for your graph, it is difficult to say without more information. It is possible that there was some error in your data or in the way you plotted the graph. It is also possible that there were other factors affecting the acceleration, such as air resistance or imperfections in the ramp or trolley. It would be helpful to compare your results to the expected values and try to identify any sources of error.