Problem 4.6
[Difficulty: 2]
Given:
Block sliding to a stop
Find:
Distance and time traveled; new coeeficient of friction
Solution:
Governing equations:
Σ
F
x
M a
x
⋅
=
F
f
μ
W
⋅
=
Assumptions:
Dry friction; neglect air resistance
Given data
μ
0.6
=
V
0
5
m
s
⋅
=
M
2 kg
⋅
=
L
2 m
⋅
=
Σ
F
x
F
f
−
=
μ
−
W
⋅
=
M a
x
⋅
=
W
g
a
x
⋅
=
W
g
2
t
x
d
d
2
⋅
=
or
2
t
x
d
d
2
μ
−
g
⋅
=
Integrating, and using I.C. V = V
0
at t = 0
Hence
dx
dt
μ
−
g
⋅
t
⋅
c
1
+
=
μ
−
g
⋅
t
⋅
V
0
+
=
(1)
Integrating again
x
1
2
−
g
⋅
t
2
⋅
V
0
t
⋅
+
c
2
+
=
1
2
−
g
⋅
t
2
⋅
V
0
t
⋅
+
=
since x = 0 at t = 0
(2)
We have the final state, at which
x
f
L
=
and
dx
dt
0
=
at
t
t
f
=
From Eq. 1
dx
dt
0
=
μ
−
g
⋅
t
f
⋅
V
0
+
=
so
t
f
V
0
μ
g
⋅
=
Using given data
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 Fall '07
 Lear
 Fluid Mechanics, Force, Trigraph, Roughness, ΣFx

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