# Motion under variable acceleration experiment

1. Nov 21, 2016

### bubblegumandcameras

Used a mass attached to a dynamic cart via pulley to examine motion under variable acceleration. As the mass was increased, my calculated friction force shows a decrease. I know that friction should increase with larger mass. Any suggestions as to why my calculations show a decrease? Used the equation Fk= mg-Mta where Mt= total mass of system, m=mass added to end of pulley, a=experimental acceleration

2. Nov 21, 2016

### Simon Bridge

Welcome to PF;
It looks like you were examining motion with variable mass - did the acceleration vary during each test run?
Did you change the mass of the cart or the mass on the end of the pulley or both (explain)?
How did you measure the acceleration?
How did you derive the equation you used?
(What assumptions did you use?)

Last edited: Nov 21, 2016
3. Nov 21, 2016

### Simon Bridge

Out of curiosity I took some guesses:
Normally you would model friction as $f=\mu mg$ for the cart ... is there friction in the pulley too?

m=mass of trolley, M=total mass, then hanging mass is M-m > m ($\mu$ needs to be measured.)

Free body diagrams for trolley accelerated by hanging mass.
(1) $T-\mu mg = ma$ for the cart
(2) $(M-m)g - T = (M-m)a$ for the hanging mass

Solve for $a$:
(3) $a = g - (1+\mu) mg/M$

experiment:
- change mass by taking weights off the trolley and adding them to the hanging mass - so M is a constant.
- measure the acceleration (time T over a fixed distance d $a=2d/T^2$)
expect the plot of $a$ vs $m$ will be a straight line with slope $s=-g(1+\mu)/M$ and intercept $g$
(does this sound like what you did?)

This allows us to calculate the friction coefficient from the measured slope.

If $f$ decreases with $m$, then $\mu$ decreases with $m$ a lot.
This will change the shape of the graph - so: plot your data - is the graph a reasonable straight line?

If not, then what sort of curve is it?
Are there systematic errors in your experiment?
ie. the above calculation neglects friction and mass in the pulley... was this a good idea?