When mass M is at the position shown, it is sliding down the inclined part of a slide at a speed of 1.99 m/s. The mass stops a distance S2 = 2.5 m along the level part of the slide. The distance S1 = 1.18 m and the angle θ = 27.70°. Calculate the coefficient of kinetic friction for the mass on the surface.
f^k = (Normal Force) * uk
mechanical energy = (potential energy: h*m*g)+(kinetic energy: 1/2m*v^2)
the general idea that kinetic friction is going to take away from the total energy.
The Attempt at a Solution
My first attempt actually involved kinematic equations, however i soon learned that this was a silly route (i will need to know at least "m" if i were to solve it this way...) So then i tried with mechanical energy...
Potential energy = h(which is 1.18sin(27.7 deg) * m * g(which is 9.8m/s^2) = 5.375m
Kinetic energy = 1/2m*v(which initially is 1.99)^2 = 1.98m
so E_mech,i = (7.355m)J and E_mech,f = 0
This also made me realize that i chose the wrong method...
Then i decided to analyze f^k a little further. I know it has a similar relationship to f = ma. This way i can effectively get rid of this whole "m" thing. However, I don't have any evidence of what the object is doing after it exits the slope. All i know is that it gains x amount of velocity going down the 27.7 deg slope in 1.18m, then it takes 2.5m of f^k to slow it down to a stop.
I then decided to try it out as a sort of work problem. I also decided to draw a straight line between x_i and x_f...
So yeah I am obviously not getting the point here. I think there is some basic info in this question that i am supposed to be paying attention to, but I'm not. This is a problem in a section where we talk about energy, power, and work. The whole thing where the object "m" suddenly goes from a theoretical acceleration due to the Normal Force minus f^k to a pure decelleration of f^k is really giving me hell. I know just about nothing about this object's movement, all i really know is that at some point it moved from the top of that slope to the x_f point in an unknown period of time.