Question

Finding the coefficient of friction,I need how I would find the friction coefficient

Answer 1

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

$\begin{gathered} ff=\mu *N \\ where\text{ }\mu\text{ is the coefficient } \\ Nis\text{ the normal force} \end{gathered}$

so, to find the coefficient we need the Normal force

if we do the sum of forces in y -axis equal zero

$\begin{gathered} N-wcos(15)=0 \\ N=wcos(15) \end{gathered}$

now, x -axis

$\begin{gathered} ff-wsin(15)=0 \\ ff=wsin(15) \end{gathered}$

finally, replace and solve for the coefficient

$\begin{gathered} ff=\mu N \\ w*sin(15)=\mu *wcos(15) \\ divide\text{ both sides by w cos\lparen15\rparen} \\ \frac{wsin(15)}{wcos(15)}=\frac{\mu *w*cos(15)}{wcos(15)} \\ \frac{sin(15)}{cos(15)}=\mu \\ tan(15)=\mu \\ 0.267=\mu \end{gathered}$

therefore, the coefficient is 0.267

I hope this helps you