# Dimensions and Dimensional analysis question

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

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

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.

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
Dimensional analysis is generally done with a few chosen "basic" dimensions. For most problems in Newtonian mechanics, length, mass and time (LMT) are sufficient. For energy, dimensions are: $E=ML^{2}T^{-2}$. The dimensional formula does not distinguish between kinetic and potential energy. Dimensionless values such as 1/2 in the KE formula do not appear in the dimensional formula.

Also, dimensional formulas do not distinguish between energy density and pressure. Both are represented by the formula $ML^{-1}T^{-2}$. 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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