Questão 12.6 - Blundell - Solução

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13/02/2021 Rinkel's modification of Ruchhardt's method | Physics Forums
https://www.physicsforums.com/threads/rinkels-modification-of-ruchhardts-method.817319/ 2/6
In Ruchhardt’s method of measuring , illustrated in Fig. 12.2, a ball of mass is placed
snugly inside a tube (cross-sectional area ) connected to a container of gas (volume ).
The pressure of the gas inside the container is slightly greater than atmospheric pressure 
 because of the downward force of the ball, so that 
 
Show that if the ball is given a slight downwards displacement, it will undergo simple
harmonic motion with period given by 
 
[You may neglect friction. As the oscillations are fairly rapid, the changes in and which
occur can be treated as occurring adiabatically.] 
In Rinkel’s 1929 modification of this experiment, the ball is held in position in the neck where
the gas pressure in the container is exactly equal to air pressure, and then let drop, the
distance that it falls before it starts to go up again is measured. 
Show that this distance is given by 
 
Homework Equations
 
The Attempt at a Solution
γ m
A V
p
p0
p = p0 +
mg
A
T
T = 2π√ mV
γpA2
p V
p
L
mgL =
γpA2L2
2V
pvγ = const.
13/02/2021 Rinkel's modification of Ruchhardt's method | Physics Forums
https://www.physicsforums.com/threads/rinkels-modification-of-ruchhardts-method.817319/ 3/6
Answers and Replies
Jun 4, 2015 #2
I have correctly derived the first equation of period of the SHM. 
From this equation, I got, 
 
As the initial velocity is 0, so 
 
Applying energy conservation for the point A & B, we get: 
 
ω2 =
pA2γ
mV
L = 2 ⋅ amplitude
mgL = 12 mω
2( L2 )
2
mgL =
pA2γL2
8V
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