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A uniform board is leaning against a smooth vertical wall. The board is at an angle above the horizontal ground. The coefficient of static friction between the ground and the lower end of the board is 0.584. Find the smallest value for the angle , such that the lower end of the board does not slide along the ground. (Please no downloadable files, my computer doesn't like them)

Respuesta :

Answer:

Explanation:

Let the board length be L

Let the board mass be m

Let the reaction force of the wall on the board be R

Let the normal force of the floor on the board be F

Let the angle from floor to board be θ

Sum vertical forces to zero

F - mg = 0

F = mg

Sum horizontal forces to zero

μF - R = 0

μF = R

Sum moments about the floor contact point to zero

R[Lsinθ] - mg[½Lcosθ] = 0

R[Lsinθ] = mg[½Lcosθ]

Rsinθ = mg½cosθ

μFsinθ = F½cosθ

μsinθ = ½cosθ

sinθ/cosθ = 1/(2μ)

tanθ = 1/(2(0.584))

θ = 40.5689606...

θ = 40.6°

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