Answer:
[tex]\mu_s=0.47[/tex]
Explanation:
Just before the box starts moving, according to Newton's first law, we have:
[tex]\sum F_x:F_f-W_x=0(1)\\\sum F_y:N-W_y=0(2)[/tex]
The sine of the angle (25°) of a right triangle is defined as the opposite cathetus ([tex]W_x[/tex]) to that angle divided into the hypotenuse (W):
[tex]sin25^\circ=\frac{W_x}{W}\\W_x=Wsin25^\circ\\W_x=mgsin25^\circ(3)[/tex]
The cosine of the angle (25°) of a right triangle is defined as the adjacent cathetus ([tex]W_y[/tex]) to that angle divided into the hypotenuse (W):
[tex]cos25^\circ=\frac{W_y}{W}\\W_y=Wcos25^\circ\\W_y=mgcos25^\circ(4)[/tex]
Recall that the maximum frictional force is defined as:
[tex]F_f=\mu_s N(5)[/tex]
Replacing (3) in (1) and (4) in (2):
[tex]F_f=mgsin25^\circ(6)\\N=mgcos25^\circ(7)[/tex]
Replacing (7) and (6) in (5) and solvinf for [tex]\mu_s[/tex]:
[tex]\mu_s=\frac{mgsin25^\circ}{mgcos25^\circ}\\\mu_s=\frac{sin25^\circ}{cos25^\circ}\\\mu_s=0.47[/tex]
