# Mercury-compensated pendulum

1. Apr 21, 2009

### SimonasV

1. The problem statement, all variables and given/known data
Mercury-compensated pendulum

A small part of Nickel tube is fulfilled with mercury.

(Alpha) Linear coefficient of expansion (Nickel)= 1x10^-5
(Beta) Volumetric coefficient of expansion (Mercury)= 18X10^-5

FIND: What part of tube should be fullfilled, that the period of the pendulum would not depend upon temperature. And there is two different cases:
a) When centre of mass coincide with centre of Mercury in that tube.
b) Include misalignment of centres...

2. Relevant equations

T=2pi(l/g)^1/2

deltaV/V=Beta*deltaT

deltaL/L=Alpha*deltaT

L=L0(1+alpha*deltaT)
V=V0(1+Beta*deltaT)

Should be more but don't know. Maybe someone could help :-)

Last edited: Apr 21, 2009
2. Apr 24, 2009

### djeitnstine

Hello simon. Would you happen to have any form of diagrams? I am having a difficult time imagining this. What is the tube connected to? Am I to assume the tube is the bob? some more details on the setup would be nice

3. Apr 24, 2009

### SimonasV

cases: a) the upper level of mercury should coincide with the mass centre of whole pendulum and b) it should not coincide.

#### Attached Files:

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4. Apr 26, 2009

### Redbelly98

Staff Emeritus
Hello SimonasV,

Think about: what is "l" in the pendulum equation?

5. Apr 27, 2009

### SimonasV

l=L - length of pendulum

6. Apr 27, 2009

### Redbelly98

Staff Emeritus
That's true if the pendulum mass is a point-mass.

However, in this example the mass occupies a region of space. So how would we define l in this case? (Hint: it's the distance from the pivot point to ______?)