the coefficient is 0.267
Explanation
Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object
Step 1
so, to graph the forces we use the Cartessian plane
let the x-axis paralle to the inclided plane
therefore,the weigth is a force acting directly to the center of the earth , ( bottomof page), so we have to find the x and y components of the weitgh
hence
the Free body diagram would be
Step 2
how to find the friction coefficient
the force of friction (ff) is given by
[tex]\begin{gathered} ff=\mu *N \\ where\text{ }\mu\text{ is the coefficient } \\ Nis\text{ the normal force} \end{gathered}[/tex]
so, to find the coefficient we need the Normal force
if we do the sum of forces in y -axis equal zero
[tex]\begin{gathered} N-wcos(15)=0 \\ N=wcos(15) \end{gathered}[/tex]
now, x -axis
[tex]\begin{gathered} ff-wsin(15)=0 \\ ff=wsin(15) \end{gathered}[/tex]
finally, replace and solve for the coefficient
[tex]\begin{gathered} ff=\mu N \\ w*sin(15)=\mu *wcos(15) \\ divide\text{ both sides by w cos\lparen15\rparen} \\ \frac{wsin(15)}{wcos(15)}=\frac{\mu *w*cos(15)}{wcos(15)} \\ \frac{sin(15)}{cos(15)}=\mu \\ tan(15)=\mu \\ 0.267=\mu \end{gathered}[/tex]
therefore, the coefficient is 0.267
I hope this helps you
