http://www.adamsavenuedesign.com/wood-wall-2/
A block of wood is held in place against a rough wall by someone pushing on it with a force directed upward?
Upward at 28° above the horizontal. The coefficients of static and kinetic friction between the wood and wall are 0.70 and 0.30, respectively. The wood slides down unless the applied force has magnitude 13 N. What is the mass of the block of wood?
? kg
There are two forces acting to keep the block from sliding down the wall:
(1) Fva, the vertical component of the applied force of 13N; and
(2) Fsf, the static friction of the block against the wall
Those forces are in balance with
(3) Fg, the weight of the block (force of gravity on the block),
From the diagram, we know that
(4) Fva = 13 * sin(28) and
(5) Fsf = Fnormal * CFsf = 13 * cos(28) * 0.70
Since the vertical forces are in balance, the downward force must = the upward, or
(6) Fg = Fva + Fsf
Since Fg = m*g, solving for the mass of the block and substituting (6) for Fg, we get
(7) m = (Fva + Fsf) / g <<========FORMULAS FOR ANSWER===
Substituting in (7) equations (4) and (5) and g = 9.8m/s^2, we get
(8) m = 13 * (sin(28) + cos(28) * 0.70) / 9.8 <<====FORMULAS FOR ANSWER===
~= 13 * (0.50 + 0.87 * 0.70) / 9.8 (approximating 28 with 30 degrees)
= 13 * (1.12) / 9.8 = 1.49Kg <<====NUMERICAL ANSWER===
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