Problem
Set 3: Problem 5.
Problem:
A single piece of cord of length
f
passes through a ring connected to a sphere of mass
m
.
The sphere rotates at constant speed,
v
, in a horizontal circular path. Noting that the tension in the cord
is the same in both portions of the cord, find
v
as a function of
f
,
θ
,
φ
and gravitational acceleration,
g
.
Solution:
The total length of the chord,
f
, is the sum of the two segments, and is thus related to the radius
of the circle,
ρ
,by
f
=
ρ
sin
φ
+
ρ
sin
θ
=
⇒
f
sin
θ
sin
φ
=
ρ
(sin
θ
+sin
φ
)=
⇒
ρ
=
f
sin
θ
sin
φ
sin
θ
φ
Now, summing forces in the vertical direction, the vertical components of the two tension forces balance
the weight of the sphere, so that
3
F
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 '06
 Shiflett
 Mass, General Relativity, Velocity

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