Environmental Engineering Reference
In-Depth Information
4.5. Sliding and rolling
In the course of a boulder's fall, the normal reflected velocity during an impact
can fall below a critical threshold or be cancelled if the coefficient of restitution is
very small: the contact then remains “permanent” and the boulder continues its
trajectory on the surface of the terrain by sliding or rolling.
4.5.1
. Sliding
In motion, the kinetic friction coefficient µ is normally a little lower than the
traditional static friction
µ
=
tg
φ.
s
On an inclined plane at angle β
(see Figure 4.8), a boulder that started at time
t
= 0 at an initial velocity
v
0
moves according to the motion equations:
dv
m
=
g
sin
β µ
−
g
cos
β
[4.24]
dt
ds
()
(
)
==−
vt
v
gt
µ β
cos
−
sin
β
[4.25]
0
dt
If µ <
tg
β, the boulder is subjected to uniformly accelerated motion.
If µ >
tg
β, the boulder is slowed down; it stops for:
ds
v
()
0
=
vt
=
0
t
=
[4.26]
1
1
(
)
dt
g
µ β
cos
−
sin
β
The distance covered before stopping is therefore equal to:
2
v
0
2c s
s
=
[4.27]
(
)
g
µ β
−
sin
β
The energy dissipated by friction is equal to the difference between the potential
energy and the kinetic energy of the boulder between
t
= 0 and
t
= 1:
2
mv
0
E
=
µ
mgs
cos
β
=
mgs
sin
β
+
[4.28]
frict
2
