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).
Materials
Pulley, hanging mass(action figure), windows movie maker, meter stick, TI-84 Graphing Calculator
Procedure
First we set up a ring stand to hang over a table so that we could maximize the distance to fall.
Attaching the pulley to the ring stand, we form a system from which we may drop a known mass (action figure).
Using a video camera, we will record the fall.
From the video, we will determine displacement versus time using the video time stamps and the meter stick using the frame by frame feature in windows movie maker.
After obtaining our set of data, we will use the quadratic regression function on the TI-84 to get the position versus time equation. Taking the second derivative of this equation will give us the acceleration of the action figure.
We may assume that the acceleration of the action figure is equal to the translational acceleration of the pulley. For this experiment we will assume friction in the pulley is negligible, and only measure the resistance to rotation via rotational inertia.
The purpose is to determine the moment of inertia of our experimental pulley to compare to the theoretical moment of inertia of a disk; 1/2*MR^2
Attaching the pulley to the ring stand, we form a system from which we may drop a known mass (action figure).
Using a video camera, we will record the fall.
From the video, we will determine displacement versus time using the video time stamps and the meter stick using the frame by frame feature in windows movie maker.
After obtaining our set of data, we will use the quadratic regression function on the TI-84 to get the position versus time equation. Taking the second derivative of this equation will give us the acceleration of the action figure.
We may assume that the acceleration of the action figure is equal to the translational acceleration of the pulley. For this experiment we will assume friction in the pulley is negligible, and only measure the resistance to rotation via rotational inertia.
The purpose is to determine the moment of inertia of our experimental pulley to compare to the theoretical moment of inertia of a disk; 1/2*MR^2
Data
Pulley
Mass: 0.0129kg
Radius: 0.0188m
Mass(Action Figure)
Mass: .0739kg
Video
Mass: 0.0129kg
Radius: 0.0188m
Mass(Action Figure)
Mass: .0739kg
Video
Time (s)0
0.035 0.07 0.105 0.14 0.175 0.21 0.245 0.28 |
Distance (m)0
0.01 0.037 0.075 0.121 0.188 0.252 0.348 0.462 |
Quadratic Regression Equation
S = 5.51t^2 + .078t + .0019
A = S'' = 11.02
S = 5.51t^2 + .078t + .0019
A = S'' = 11.02
Analysis
Theoretical Moment of Inertia
Iα = Στ = R(ma)
ΣF = ma =
Iα = Στ = R(ma)
ΣF = ma =
Conclusion
Our method of measuring the translational acceleration of our object seemed to be ineffective as we measured an acceleration greater than that of gravity. Our super hero defied the laws of physics, as his cape brought him closer to earth with an increased, rather than decreased speed.
Therefore, it was apparent that our experimental value for moment of inertia of a pulley would not be consistent with that of a disk ( I = 1/2 MR^2 ). Instead we arrived at a moment of inertia equal to:
Possible sources of error could be mislabeled time stamps on the video, inconsistencies in the measuring process, and also a very indistinct displacement on the video. Due to a poor quality camera, when dealing with frames 35ms apart, there was a significant amount of blur in the picture, making it difficult to judge just how far the object had fallen. This is likely the greatest source of error as the lowest point recorded may have been a shadow of rather than the actual object.
The experiment ought to be repeated additional times, perhaps using a motion detector in order to achieve more accurate results.
Therefore, it was apparent that our experimental value for moment of inertia of a pulley would not be consistent with that of a disk ( I = 1/2 MR^2 ). Instead we arrived at a moment of inertia equal to:
Possible sources of error could be mislabeled time stamps on the video, inconsistencies in the measuring process, and also a very indistinct displacement on the video. Due to a poor quality camera, when dealing with frames 35ms apart, there was a significant amount of blur in the picture, making it difficult to judge just how far the object had fallen. This is likely the greatest source of error as the lowest point recorded may have been a shadow of rather than the actual object.
The experiment ought to be repeated additional times, perhaps using a motion detector in order to achieve more accurate results.