The coefficient of static friction between a block of wood of mass 29.2-kg and a rough table is 0.51. The table is slowly tilted until the block of wood starts to slide down the surface. At what angle of the table with respect to the horizontal does the wood start to slide? Your answer should be given to the nearest tenth of a degree.

Question

The coefficient of static friction between a block of wood of mass 29.2-kg and a rough table is 0.51.  The table is slowly tilted until the block of wood starts to slide down the surface.  At what angle of the table with respect to the horizontal does the wood start to slide?  Your answer should be given to the nearest tenth of a degree.

Henry · Answer

Ww = m*g = 29.2kg * 9.8N/kg = 286.2 N. =
Wt. of the wood.

Fp = 286.2*sinA = Force parallel to incline.
Fv = 286.2 *cosA = Force perpendicular to incline.

286.2*sinA-0.51*286.2*cosA = m*a
286.2*sinA -146*cosA = m*0 = 0.
286.2*sinA = 146*cosA
Divide both sides by cosA:
286.2*(sinA/cosA) = 146
Replace sinA/cosA with tanA:
286.2*tanA = 146
tanA = 0.51013.
A = 27.0o.