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57. Problem 13.53P (HRW) A rectangular slab of slate rests on an
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incline.
The slab has dimensions 43 m long, 2.5 m thick and 12 m
wide. Its density is 3.2
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The coefficient of static friction between the slab and the underlying rock
is 0.39. (a) Calculate the component of the slab’s weight acting parallel
to the incline. (b) Calculate the static frictional force on the slab. By
comparing (a) and (b), we can see that the slab is in the danger
of sliding and is prevented from doing so only by chance protrusions between the
slab and the underlying rock. (c) To stabilise the slab, bolts are driven
perpendicular to the incline. If each bolt has a cross-sectional are of 6.4
cm2 and will snap under a shearing stress of
,
what is the minimum numbers of bolts needed? We can assume that the bolts do
not affect the normal force. 
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Solution: Click For PDF Version Volume of the slab,
Density of slate,
Weight of the slab,
Free-body diagram of the slab is
(a) Component of slab’s weight acting parallel to the incline (b) Maximum force of static friction,
By comparing (a) and (b), we note that the maximum force of static friction is less than the component of the weight parallel to the incline.
(c) Each bolt can withstand a force
Therefore, the number of bolts needed for holding the slab on the incline Therefore, the minimum number of bolts required for holding the slab on the incline will be 16. |
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