E = 1/2 mv^2 solve for m

Question

terenzreignz · Answer

Solving for certain values...  slowly becoming a forgotten art...

Nevertheless, we're here to make sure it doesn't fade into obscurity...
The trick is to put the addition and multiplication properties of equality to good use...
$$\LARGE E = \frac12 mv^2$$
Okay, so our goal here to to isolate the m value (in other words, manipulate the equation such that m stands alone on one side).

Currently, it is accompanied by a $\large \frac12$  and a $\large v^2$
So we sort of have to "get rid" of those two values, by bringing them to the other side...

Since this just involves multiplication, we use the multiplication property of equality... in particular, what can we multiply to $\Large \frac12 mv^2$  to get rid of the $\large \frac12$  ?

anonymous · Answer

I have m = 2E/V^2 but stuck after that. Do I apply a square root on both sides then?

terenzreignz · Answer

Oh, I see you're way ahead of me... so you arrived at
$$\LARGE m = \frac{2E}{v^2}$$
right?

Well that's already it.  That's the answer, unless we have specific values for E and v :)

anonymous · Answer

If I was given a value for v already, do I square that value or is the value already squared?

terenzreignz · Answer

No, you plug it into v, and do whatever was done to v...

If an example helps, if we're given v = 2 then...
$$\Large m = \frac{2E}{v^2}= \frac{2E}{\color{red}2^2}=\frac{2E}{\color{red}4}$$

anonymous · Answer

Ok, that's very helpful! thank you!

terenzreignz · Answer

No problem :)