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(c) The assumption is no longer that the slope of the bottom of the slide is horizontal, but
rather that the slope of the top of the slide is vertical (and 12 m to the left of the center of
curvature). Returning to the pendulum analogy, this corresponds to releasing the
pendulum from horizontal (at
θ
1
= 90° measured from vertical) and taking a snapshot of
its motion a few moments later when it is at angle
2
with speed
v
= 6.2 m/s. The
difference in height between these two positions is (just as we would figure for the
pendulum of length
R
)
Δ
hR
R
R
=−
−−
=
−
11
21
2
cos
cos
cos
θθ
bg
where we have used the fact that cos
1
= 0. Thus, with
Δ
h
= –4.0 m, we obtain
2
=70.5°
which means the arc subtends an angle of 
Δ
 = 19.5° or 0.34 radians. Multiplying this
by the radius gives a slide length of
s'
= 4.1 m.
(d) We again find the magnitude
f '
of the frictional force by using Eq. 831 (with
W
= 0):
0
1
2
2
=++
+
′′
ΔΔΔ
KUE
mv
mgh
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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

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