A crate is placed on an inclined board as shown in the figure below. One end of
ID: 2136416 • Letter: A
Question
A crate is placed on an inclined board as shown in the figure below. One end of the board is hinged so that the angle ? is adjustable. If the coefficient of static friction between the crate and the board is ?S = 0.25, what is the value of ? at which the crate just begins to slip?
Explanation / Answer
The weight of the crate can be resolved into a normal force (N), and a parallel force F:
F = m*g*Sin(?)
N = m*g*Cos(?)
The friction force, Ff is ?N
Ff = ?*m*g*Cos(?)
The crate is just about to slide when F = Ff
?*m*g*Cos(?) = m*g*Sin(?)
the m*g cancels out:
?*Cos(?) = Sin(?)
? = Sin(?)/Cos(?) = Tan(?)
? = Atan(?) = 14.04 degrees
assuming of course that ? is the angle between the board and the horizontal.
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