Newton's Laws of Motion Lab Question

[Elkay]

I performed a lab where I had to find the acceleration of two masses that were connected by a string and hanging on a pulley. The equation used was:
http://home.earthlink.net/~copper017/Random/PhysicsLab/acceleration.jpg



After performing the calculations I got the following data:
http://home.earthlink.net/~copper017/Random/PhysicsLab/data.jpg



Looking at my data, I noticed that as M1 and M2 became closer in mass, the percent difference between the experimental acceleration and the theoretical acceleration became larger and larger. I don't quite understand why that would happen. My lab instructor tried to explain it to me, but I didn't get it. So I'm hoping that someone here could help. Thank you.

 

[mybsaccownt]

hmm...

it would seem that as m1 and m2 approach the same value then the acceleration of the system will get closer to 0

since the forces on both sides of the pulley would be balanced

that's fine, but you're not actually setting the masses exactly equal, and so you should have some acceleration, the theoretical one you calculated

however...when you are actually measuring this in a real world setting and the acceleration is getting quite small, well then the other factors start to play a larger role

the other factors being: the inertia of the pulley, the friction between the pulley and the string, and the friction of the bearing in the pulley, and I suppose if you were taking incredibly accurate measurements (perhaps the strain that the masses cause in the string, and the air resistance and...blah blah, lol)

in doing the theoretical calculations, you did not take these factors into account...but as you see from the values in the actual experiment, they are there

however, if the difference between m1 and m2 is quite large, then these factors are basically negligible and that's why your values for the greater differences between the masses are closer to the theoretical value

 

[m2003]

I would first like to commend you on your well-designed experiment and accurate data collection. Your results clearly show a relationship between the masses and the acceleration, as predicted by Newton's Second Law of Motion (F=ma).

The increase in percent difference between the experimental and theoretical accelerations as the masses become closer in value is likely due to experimental error. In this case, the error could be caused by the string not being perfectly taut, the pulley not being completely frictionless, or human error in measuring the masses or timing the motion. As the masses become more similar, even small errors can have a larger impact on the results.

To minimize these errors, it is important to carefully control and measure all variables in the experiment. Additionally, repeating the experiment multiple times and taking an average of the results can help to reduce the impact of any individual errors.

Overall, your experiment and results demonstrate the fundamental principles of Newton's Laws of Motion and the importance of careful experimental design and data analysis in scientific research. Keep up the good work!