Background/Experiment setup: In one of my classes a mass (0.04 kg) was hung from a pulley and attached to a much heavier mass (around 0.4 kg) that rest on an airtrack. A thread connected the hanging mass with the one on the track.
The hanging mass would be dropped and the acceleration of the mass on the airtrack would be calculated. For 5 trials the mass was increased .01 kg and the acceleration calculated.
Then I divided gravity by each calculated acceleration so I ended up with 6 new numbers. Then for each mass I divided $m_1$ ($0.4$ kg) by each hanging mass. Then I plotted $\frac{m_1}{m_2}$ as the $x$ axis of a graph and $\frac ga$ as the $y$ axis.
Then I found a line of best fit:
$y = 1.0004x + 0.99 $
$r^2 = 0.9994. $
So it produces a very straight line, the data line up very well and produce a great line of best fit.
Question: How does this verify Newton's 2nd law? I understand that it is $F=ma$, and the graph does show that as mass increases so does acceleration proportionally. IS all that is needed to verify it? I'm having a hard time in my lab write up actually explaining how this set up verifies Newton's 2nd law.
Thanks for reading!
Best Answer
Yes. Newton's second law $\Leftrightarrow$ Force is proportional to mass with the acceleration being the constant of proportionality.
Since it's a straight line, this implies proportionality.