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which yields
f
k
= 47 N. We also apply Newton’s second law to the
y
axis (perpendicular
to the incline surface), where the accelerationcomponent is zero:
140cos25
0
127 N.
NN
FF
−°
=
¡
=
Therefore,
μ
k
=
f
k
/
F
N
= 0.37.
(b) Returning to our first equation in part (a), we see that if the downhill component of
the weight force were insufficient to overcome static friction, the child would not slide at
all. Therefore, we require 140 sin 25° >
f
s
,max
=
s
F
N
, which leads to tan 25° = 0.47 >
s
.
The minimum value of
s
equals
k
and is more subtle; reference to §61 is recommended.
If
k
exceeded
s
then when static friction were overcome (as the incline is raised) then it
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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, Mass

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