When mass M is at the position shown, it is sliding down the inclined part of a

Question

   When mass M is at the position shown, it is sliding down the inclined part of a  slide at a speed of 1.97 m/s. The mass stops a distance  S2 = 2.5 m along the level part of the slide.  The  distance S1 = 1.17 m and the angle ? =  29.10 When mass M is at the position shown, it is sliding down the inclined part of a slide at a speed of 1.97 m/s. The mass stops a distance S2 = 2.5 m along the level part of the slide. The distance S1 = 1.17 m and the angle ? = 29.10Degree. Calculate the coefficient of kinetic friction for the mass on the surface.

Explanation / Answer

let F1 and F2 be friction forces at surface S1 and S2 respectively.
we have that
mv0^2/2 + m*S1*sin0*g = F1*S1+F2*S2 (conservation of energy).
Where F1 is clearly equal to mg*cos0*k and F2 = mg*k
where k is the coefficient.
we have that
k*mg*(cos0*S1+S2)=mv0^2/2+m*S1*sin0*g
so k *g(cos0*S1+S2)=v0^2/2+S1*sin0*g.
so k=0.21776

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