- #1
fluidistic
Gold Member
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Hi,
I've done the problem but I'm unsure of my answer. I would be glad if you could check it out.
A steal pendulum is considered a clock at a certain temperature.
What is the maximum variation of temperature we can submit to the pendulum if it cannot delay more than one second by day?
First I notice that a period of the pendulum corresponds to a second. Then I calculated the number of seconds in day to be 86400.
Say it delays 1 second in a day and I want to calculate its period. We have that [tex]86400T=86401T'[/tex]. Replacing [tex]T[/tex] with [tex]2\pi \sqrt {\frac{g}{l}}[/tex] then I get that [tex]l'=0.9999768523l[/tex] where [tex]l[/tex] is the length of the pendulum and [tex]l'[/tex] the length of the heated pendulum.
Now I want to find the length it cannot overpass : [tex]l(1-0.9999768523)=0.00002314774628l[/tex].
Looking at the coefficient of dilation of steal, if I heat the pendulum by 1°C, it will grow [tex]0.0000011l[/tex]. From it, I just look and see that I can heat the pendulum up to 23°C more than it is.
To my intuition it looks too much. What do you say?
I've done the problem but I'm unsure of my answer. I would be glad if you could check it out.
Homework Statement
A steal pendulum is considered a clock at a certain temperature.
What is the maximum variation of temperature we can submit to the pendulum if it cannot delay more than one second by day?
Homework Equations
Coefficient of dilation of steal : [tex]11\times 10 ^{-6}°C^{-1}[/tex].The Attempt at a Solution
First I notice that a period of the pendulum corresponds to a second. Then I calculated the number of seconds in day to be 86400.
Say it delays 1 second in a day and I want to calculate its period. We have that [tex]86400T=86401T'[/tex]. Replacing [tex]T[/tex] with [tex]2\pi \sqrt {\frac{g}{l}}[/tex] then I get that [tex]l'=0.9999768523l[/tex] where [tex]l[/tex] is the length of the pendulum and [tex]l'[/tex] the length of the heated pendulum.
Now I want to find the length it cannot overpass : [tex]l(1-0.9999768523)=0.00002314774628l[/tex].
Looking at the coefficient of dilation of steal, if I heat the pendulum by 1°C, it will grow [tex]0.0000011l[/tex]. From it, I just look and see that I can heat the pendulum up to 23°C more than it is.
To my intuition it looks too much. What do you say?