Friction is one of the most important forces studied in classical mechanics, and still is the subject of pedagogical literature. In a small series of problems stated below, we consider a particle sliding down a curve under the actions of gravity and kinetic friction. Unlike many of the referenced sources, we neglect the centripetal force arising on the curved portions of the incline (i.e., assume that the centripetal acceleration is much smaller than g) and, instead of parameters such as the location of the release point of a particle, concentrate on the horizontal displacement of the particle.

1.
D.
Van Domelen
, “
Showing area matters: A work of friction
,”
Phys. Teach.
48
,
28
(
Jan.
2010
).
2.
F.
González-Cataldo
,
G.
Gutiérrez
, and
J.M.
Yáñez
, “
Sliding down an arbitrary curve in the presence of friction
,”
Am. J. Phys.
85
,
108
114
(
Feb.
2017
).
3.
A.
Aghamohammadi
, “
The point of departure of a particle sliding on a curved surface
,”
Eur. J. Phys.
33
,
1111
1117
(
2012
).
4.
T.
Prior
and
E.J.
Mele
, “
A block slipping on a sphere with friction: Exact and perturbative solutions
,”
Am. J. Phys.
75
,
423
426
(
May
2007
).
5.
G. E.
Hite
, “
The sled race
,”
Am. J. Phys.
72
,
1055
1058
(
Aug.
2004
).
6.
We consider the case of μ < [y(0) – y(xb)]/ xb, when, according to Eq. (6), xf > xb.
7.
James
Stuart
,
Calculus
, Vol.
1
, 8th ed. (
Cengage Learning
,
Boston
,
2016
), pp.
528
531
.
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