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Dimensions and Dimensional analysis question 
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#1
Oct2613, 07:28 PM

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In this formula, E = 1/2 mv²
1/2 is not considered as it does not have any dimension. But then does it not affect the formula. Why? Explain!! Please 


#2
Oct2613, 07:54 PM

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P: 13,124

Welcome to PF;
Of course the value of 1/2 affects the formula... what is there to explain? 


#3
Oct2613, 08:06 PM

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P: 1,948

That's a limitation of dimensional analysis. numerical factors such as 1/2 in the formula for the kinetic energy cannot be calculated by dimensional analysis. Some more advanced calculation method must be used.



#4
Oct2613, 08:15 PM

P: 2,504

Dimensions and Dimensional analysis question
Also, dimensional formulas do not distinguish between energy density and pressure. Both are represented by the formula [itex]ML^{1}T^{2}[/itex]. The difference is that energy density is a scalar quantity and pressure is a vector quantity. DA is useful in showing relationships between different formulas used in physics. That doesn't mean that different formulas with the same dimensional formula are necessarily strictly equivalent. They may only be dimensionally equivalent. 


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