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21. If the block is sliding then we compute the kinetic friction from Eq. 62; if it is not
sliding, then we determine the extent of static friction from applying Newton’s law, with
zero acceleration, to the
x
axis (which is parallel to the incline surface). The question of
whether or not it is sliding is therefore crucial, and depends on the maximum static
friction force, as calculated from Eq. 61. The forces are resolved in the incline plane
coordinate system in Figure 65 in the textbook. The acceleration, if there is any, is along
the
x
axis, and we are taking uphill as +
x
. The net force along the
y
axis, then, is certainly
zero, which provides the following relationship:
0c
o
s
yN
FF
W
θ
=
¡
=
¦
G
where
W
=
mg
= 45 N is the weight of the block, and
= 15° is the incline angle. Thus,
F
N
= 43.5 N, which implies that the maximum static friction force should be
f
s
,max
= (0.50) (43.5 N) = 21.7 N.
(a) For
ˆ
( 5.0 N)i
P
=−
G
, Newton’s second law, applied to the
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Acceleration, Friction

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