Hi, How to show that Newton's second law for dimensional homogeneity. thanks
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Originally Posted by hazeleyes Hi, How to show that Newton's second law for dimensional homogeneity. thanks You need to show that the units match on both sides of the equation. Force has units Now we need to take the derivative on the right hand side So now analyze the units So the units on both sides are the same
Originally Posted by TheEmptySet You need to show that the units match on both sides of the equation. Force has units Now we need to take the derivative on the right hand side So now analyze the units So the units on both sides are the same May I ask how is mass a function of time?
Originally Posted by bugatti79 May I ask how is mass a function of time? OK, it could be the a mass flow rate like density by the cross sectional area by velocity
Originally Posted by bugatti79 May I ask how is mass a function of time? With rockets, you are ejecting mass to propel yourself forward. Mass is most definitely a function of time then. The most general form of Newton's Second Law is the version in his Principia:
Originally Posted by TheEmptySet You need to show that the units match on both sides of the equation. Force has units Now we need to take the derivative on the right hand side So now analyze the units So the units on both sides are the same but isn't Volume flow rate(dv/dt)=
In Newton's Second Law, v is velocity, not volume. So it would have units of m/s. Usually, volume is an upper-case V (math is case-sensitive!).
but why dm/dt is kg/s?
Originally Posted by hazeleyes but why dm/dt is kg/s? It is the change is mass with respect to time so the units are mass over time or kg/s
Thanks so much!!
Originally Posted by TheEmptySet It is the change is mass with respect to time so the units are mass over time or kg/s More generally, if I have a function and the units of are and the units of are then the units of are Similarly, the units of are