Finding Mass from slope?

Question

This goes with Newton's Second Law. I need to know how to find mass (M) by converting this equation t2 = 2*(½ at2) / [(mg) / (M + m)] into a form where it turns into slope=*something*, then M = *something*/slope? (Frictionless Airtack on Level plane)

Answer 1

You've asked this question poorly.

For starters, if you mean:
t² = 2 * (½ at² ) / [mg/(M+m)]
then this reduces to
1 = a / [mg/(M+m)] = a(M+m)/mg

And what slope do you mean? The only derivative in that equation is a if it stands acceleration. I'm going to go ahead and assume that you mean you've done an experiment where you have several pairs of correlating values, and you need to plot these to determine an approximate value that can be used in that equation. In that case, you'd need to plot the points using scales such that it will produce a linear relationship. Your equation does not make sense so I cannot determine what the axes should be. But in a situation where y is proportional to x² (an equation like y = ax² ) and you need to determine what the proportionaly constant is using values of x and y that you have measured, plot y against x² (square the values before plotting them) and you will get a straight line which you can graphically estimate the slope from.

From your equation, I'm guessing that all of 1/[(mg)/(M+m)] is your proportionality constant. By plotting whatever the othe variables are meant to be, you can determine the slope of the graph and hence the value of the above term. Since you should know the other values in that term, you can set that term equal to its estimated value and rearrange it for the unknown.