Experiment
Using an Atwood's machine, in a one-man "group", I calculated the percent errors between calculated and actual acceleration for 2 hanging masses of different measures (but equal difference in net force).
Theory & Creation
It's concept originating in 1784, this construction produced by George Atwood was used to confirm the mechanical laws of motion, using the constant acceleration between the two hanging masses. Though not present in reality, but still used for this experiment, the idea behind it uses the concept of an "ideal pulley", using a mass-less string and system and lacks a friction.
To right: Atwood's Device FBD |
Experimental Technique
To begin the experiment, a FBD must first be constructed (above). Giving the different variables their own respective places, we can now start the work, seen to the right.
Now having the true equation for acceleration, we can now take the measurements for mass and acceleration on the Atwood Device. All masses have a net difference of 5 g. 1.) 210 g & 205 g / a = 0.084 m/s² 2.) 160 g & 155 g / a = 0.130 m/s² 3.) 130 g & 125 g / a = 0.158 m/s² 4.) 110 g & 105 g / a = 0.200 m/s² 5.) 80 g & 75 g / a = 0.256 m/s² 6.) 60 g & 55 g / a = 0.389 m/s² 7.) 30 g & 25 g / a = 0.708 m/s² 8.) 20 g & 15 g / a = 1.03 m/s² 9.) 15 g & 10 g / a = 2.56 m/s² 10.) 10 g & 5 g / a = 2.18 m/s² Compare these to the calculated answers, which are: 1.) a = 0.118 m/s² 2.) a = 0.156 m/s² 3.) a = 0.192 m/s² 4.) a = 0.228 m/s² 5.) a = 0.316 m/s² 6.) a = 0.426 m/s² 7.) a = 0.891 m/s² 8.) a = 1.40 m/s² 9.) a = 1.96 m/s² 10.) a = 3.27 m/s² And finally, putting these into the equation for %-error below, we can then get our answers... %-error = [ 2(t - a)/(t + a)] x 100% 1.) 33.7% 2.) 18.2% 3.) 19.4% 4.) 13.1% 5.) 20.1% 6.) 9.08% 7.) 22.9% 8.) 30.5% 9.) 26.5% 10.) 40.0% |
Analysis
Seeing as the %-errors tend to follow a bell curve, with the most accurate being the centerpoint, there are many factors to take into consideration as to why this happened. For the higher masses, the most reasonable idea behind the large inaccuracy is the net difference in forces. Because of such a small difference for the large forces, and thus a small acceleration, friction was able to change the actual answer from the calculated answer quite severely. The same is true for the other side, where friction had a large playing part in the small masses. However, for the smallest masses, the largest playing role was the inaccuracy of the motion sensor, where it could not track the velocity (and acceleration which is based off it) and thus gave an incorrect answer, plainly seen by it's acceleration being less than the 9th trials.
Conclusion
All around, the experiment was a success. Though the %-errors were a bit wonky due to specific inaccuracies, the general idea of the experiment was still reached. Even with an equal difference in forces between masses, the change in the masses caused a change in acceleration, where the larger the actual proportion of mass between the weights, the larger the acceleration.