I am working on the analysis portion of a lab. The experiment was dropping varying masses connected to a cart by a string and pulley. The cart's mass was constant in each trial, but the hanging mass was increased each trial. We were measuring the acceleration of the cart. Graphing our acceleration data vs. mass1 / (mass1 + mass2) gives us a linear looking line. Using a curve fit in graphical analysis program, we can see the slope is around 9.0 m/s/s. This slope relates to gravity. However it is not actually g because of the friction that is slowing the system down. Now here is the question I am stuck on: Find an equation that you can use to graph your existing experimental data to estimate g and f (force of friction). Regraph your data using this equation and use linear fit to estimate g and f. I am stuck here. The idea is that accounting for friction gives a more accurate estimation of g (gravity). But I don't know what to do. I realize I could solve for f by assuming g = 9.8 but that is not the point. I need to get g through graphing my data somehow.
The Attempt at a Solution
I figured out that I can expand on a = m1(g) / (m1+m2) by adding friction. I got:
a = (m1(g) - f) / (m1+m2)
where a = acceleration
m1= hanging mass
m2 = cart on track
f = force of friction
I'm trying to see how I can use this to work out an equation or a way to graph my data but I don't see how. I thought maybe acceleration could be y-axis, m1/(m1+m2) could be x, gravity could be slope (m), and y-intercept (b) would be the acceleration loss due to friction. But i'm not sure how to graph my data and get the results I want. How am I supposed to do this?