Lab+10+-+Atwood's+Machine

= **__Lab 10 - Atwood's Machine__**  =

This lab was conducted in the interest of discovering the relationship between different masses in a system and the overall acceleration of the system. In this experiment, weight increments are known and for the sake of simplicity, the pulley is assumed to have zero friction and zero mass. The string used was also assumed to have zero friction and zero mass for identical reasons. While these are not true, these problems were compensated for by using very low friction pulleys and very light string.
 * Purpose/Background**

It is hypothesized that the acceleration of the system will increase in a relatively linear manner due to the fact that the total weight of the system is maintained and the only thing that was changed was the distribution of the weights. When the total weight of the system is altered, it is predicted that the acceleration will decrease with more trials since as the weights get larger, the fixed difference between them will become insignificant thus generating a situation where the acceleration of the system will approach zero.
 * Hypothesis**


 * Apparatus**
 * Computer
 * Logger Pro
 * Vernier Computer Interface
 * Vernier Photograte with Ultra Pulley
 * Masses
 * "Seemingly Massless" String
 * Utility and Perpendicular Clamps
 * Ring Stand
 * Cups
 * Paperclips


 * Procedure**
 * 1) The Vernier Photogate Ultra Pulley was assembled and plugged into the computer via the Vernier Computer Interface.
 * 2) Varying masses were placed into the appropriate cups. The lighter of the two cups (m1) was placed near the ground allowing the second of the two cups (m2) to be positioned approximately 40cm above the ground.
 * 3) The masses were released and the data were acquired using Logger Pro's interface.
 * 4) Since the data were recorded as measures of velocity, using the Linear Fit function in Logger Pro allowed for the slope of the velocity to be found, otherwise known as the acceleration.
 * 5) The masses were reallocated according to various instructions.
 * 6) Steps 2-5 were repeated as needed.


 * Data**

m1 + m2 = mT ; 200g + 200g = 400g ; The total mass (mT) of the system is found by adding the two involved masses. Considering that the linearity and the R^2 value of the first graph, the data seem reasonable. However, for the latter graph, the value for the acceleration seemed unusually high with a value of 1.014m/s/s when the next highest acceleration was 0.600 m/s/s. It is believed that this particular datum point's unusually high value was due partly to a faulty data acquisition system and failure to closely manage mass allocation.
 * Analysis**
 * m2 - m1| = ∆m ; 210g - 190 g = 20g ; The change in mass (∆m) is calculated by subtracting the smaller mass from the larger mass.

Preliminary Questions: 1) If two equal masses are suspended from either end of an Atwood's machine, it is inferred that the velocity would be a constant zero thus creating no acceleration. This is believed because there is no net force that is not accounted for or cancelled out if the pulley is equally weighted. 2) Moving one mass from one side to the other while keeping the mass constant would most likely result in acceleration of the system to become a non zero number. The acceleration would most likely increase steadily since mass and acceleration are inversely proportional according to Newton's 2nd law of motion. Gradually increasing the mass of both sides would most likely result in an acceleration that sloped downward. This is believed because if thought of as a limit, as the weight of the masses approaches larger numbers, the 20g difference between the two masses will become insignificant which would result in the "leveling out" of the accelerations to approach zero. 3) Acceleration due to gravity never changes. Also, the acceleration of the system is conserved and is opposed equally to the other forces in the system. 4) If only I could draw free-body diagrams on here...

Analysis Questions: 1) See graphs. 2) See graphs. 3) The relationship between the mass difference and acceleration in an Atwood's machine is a positive correlation. This means that as ∆m increases, acceleration of the system also increases. 4) The relationship between the total mass and the acceleration in an Atwood's machine is a negative correlation. This means that as mT increases, the acceleration of the system tends to decrease. This is what was expected had the data acquisition gone as planned.

Overall, the original hypothesis was supported. For Part I when the total mass was held constant, changing the mass from the lighter mass (generally named m1 in this case) to the more massive mass (m2) changed the acceleration because there is no longer a non zero net force since the one side of the Atwood's machine weighed more. Seeing that the mass of the system did not change, this means acceleration must have been a non zero number greater than zero. This is evident in the first graph where increasing the difference between the masses with each trial caused the acceleration to increase in a linear fashion. For Part II when the mass difference was held constant but the total mass of the system was changed, the constant mass difference (20g) indicates that the net force was not varied. Since the masses increased, and mass and acceleration are inversely proportional to each other in Newton's 2nd law of motion F = ma, this means that as mass increased, the acceleration must have decreased which would have been evident in the second graph had the acceleration for m1 = 180g and m2 = 160g been accurately captured. Since the data were not as expected for Part II, should this experiment be conducted again in the future, more trials would have been performed to ensure more accurate data acquisition.
 * Conclusion**

©Kevin Trinh 2011