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Can Constants with Variables Cancel Out to Create a Constant?
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[QUOTE="Simon Bridge, post: 4603343, member: 367532"] Welcome to PF; It is possible that a combination of variables will be a constant for the situation at hand. But that is not the case for your problem. You are supposed to get to: $$f=\sqrt{ \frac{F}{4\pi^2mr}}\qquad\text{...(1)}$$... (check that - it does not look right to me) from: $$\begin{align}f^2\propto F & \qquad\text{...(2)}\\ f\propto \frac{1}{m} & \qquad\text{...(3)}\\ f\propto \frac{1}{r} & \qquad\text{...(4)} \end{align}$$ You get $$f^2=k\frac{F^2}{m^2r^2}$$ and ask:... No - it cannot be. ##k## has to be a [i]constant[/i] - I don't expect that the product ##mr## is a constant You have another step to perform before you put in the constant of proportionality. You want to find an equation for ##f## and what you have so far is an equation for ##f^2##. What do you have to do to your equation to turn it into an equation for ##f##? Edit: I think I see your problem - which is why I suggest you check the first equation. [/QUOTE]
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Can Constants with Variables Cancel Out to Create a Constant?
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