Purpose
Measure the translational acceleration of a object falling from a pulley (as illustrated in the figure below), and
Use the measured acceleration to analyze the validity of assumption that the pulley exhibits rotational inertia consistent with a disk (I = ½ MR2).
Use the measured acceleration to analyze the validity of assumption that the pulley exhibits rotational inertia consistent with a disk (I = ½ MR2).
Equipment
Pulley, hanging mass, motion detector with CBL data acquisition system.
Procedure
In order to measure the acceleration of the action figure we first clamped a rod to the table and hung a pulley off of the end of it. Directly below the pulley we had our data acquisition system (motion detector). We attached out mass (an action figure) to a string which we wound up around the pulley. We released the action figure and started the recording device.
Data
Data Analysis
Using the distance vs time graph above we can find the velocity and acceleration equations by taking the derivative(or finding the slope) and second derivative. Using various equipment we measured the radius of the wheel to be .01875m and the mass to be .0129kg. We also found the mass of the action figure to be .0721. One possible change to the experiment could be: use a computerized dropping mechanism that would drop the mass at the exact time the motion detector started recording, we had to do 2 or 3 trials just to get our timing down so that we could get usable data.
Conclusion
In this lab we found the translational acceleration of an object falling from a pulley and then used it to test the I=1/2*m*r^2 equation. Unless variables such as friction mass of the string possible slipping and other objects interacting with the motion detector accounted for a 59.65% error, which I wouldn't expect them to cause such a high % error, then the equation I=1/2*m*r^2 did not work for our experiment.