Question

Instructor Sanchez leans a ladder of length 1 against the side of a wall as shown. If the angle that the ladder makes with the horizontal is 69°, find the minimum coefficient of static friction that will keep the ladder from sliding. Note there are two normal forces, one from the floor and one from the wall. Do not neglect the weight of the ladder and assume there is no friction along the vertical wall. the ladder is in static equilibrium.

Answer 1

Answer:thanks

Step-by-step explanation:

Answer 2

`\begin{gathered} \text{From the fr}ee\text{ body diagram} \\ \uparrow+\Sigma Fy=0 \\ N2-mg=0 \\ N2=mg \\ \rightarrow+\Sigma Fx=0 \\ Fr-N1=0 \\ \text{Hence} \\ Fr=N1 \\ \text{But} \\ Fr=N2\cdot\mu \\ \text{Also} \\ N2=mg \\ Fr=mg\cdot\mu \\ \text{Therefore} \\ N1=mg\cdot\mu \\ \\ \text{Counterclockwise }+ \\ \Sigma M_A=0 \\ N1\cdot L\sin (69)-(mgL\cos(69))/(2)=0 \\ N1\cdot L\sin (69)=(mgL\cos(69))/(2) \\ N1\cdot\sin (69)=(mg\cos (69))/(2) \\ N1=(mg\cos (69))/(2\sin (69)) \\ N1=(mg)/(2)\cot (69) \\ \\ \text{Therefore} \\ N1=mg\cdot\mu \\ (mg)/(2)\cot (69)=mg\cdot\mu \\ \mu=(\cot (69))/(2) \\ \mu=0.192 \\ \text{The value of coeficiente static friction is }0.192 \end{gathered}`