Roth+Lab+10+Atwood's

Lab 10 Atwood’s Machine
 * Purpose**: The purpose of this lab is to discern the relationship between changes in mass and acceleration using and to become familiar with using and making calculations using an Atwood’s machine.
 * Hypothesis**: It is hypothesized that a greater difference in mass between the two masses connected to the Atwood’s machine would contribute to a greater acceleration. It is also hypothesized that no motion would occur if two equal masses were suspended from either end of the string on an Atwood’s machine. This is because the masses would be equal, and the accelerations would both be zero, which would make the net force equal to zero. It is hypothesized that increasing the masses of both sides equally will not have an effect on the acceleration because it would not change the difference in masses. The difference in masses would remain constant. Two equal masses would have the same acceleration because they have the same mass and force of gravity. Therefore, they have the same weight, The force of gravity would act equally on both of them, so the accelerations would be the same.
 * Apparatus**: The following tools were used to carry out this lab.
 * Vernier Photogate with Ultra Pulley
 * Mass Set
 * String
 * Computer
 * Vernier Computer Interface
 * Logger Pro
 * Procedure**:
 * 1) Set up the Atwood’s machine apparatus so that the string that is wrapped around the wheel can move at least 40 cm before touching the floor.
 * 2) Connect together the Photogate and the DIG/SONIC 1 of the interface.
 * 3) Open a velocity vs. time graph in Logger Pro.
 * 4) Attach cups to the strings in the pulley system and put 200g in each cup. Record the masses and accelerations.
 * 5) Move 5g from one cup to another and record the masses and acceleration produced.
 * 6) Keep moving 5g from the cup that you originally removed 5 grams from until you have 5 unique differences in mass.
 * 7) Record the masses and accelerations from each combination.
 * 8) Remove the masses from the cups and put 120g in the first cup and 100 g in the second cup. Record the masses, and acceleration produced by the Atwood’s machine. Then subtract the second mass from the first mass to calculate the difference in masses. Add the two masses to calculate the total mass.
 * 9) Put an additional 20g in each cup 4 more times and record the masses, difference in masses, total mass, and acceleration each time.

Change in Mass= Mass 1 – Mass 2 Total Mass= Mass 1 + Mass 2
 * Data:**
 * Total Mass Constant ||
 * Trial || Mass 1 (g) || Mass 2 (g) || Acceleration (m/(s^2)) || Change in Mass (g) || Total Mass (g) ||
 * 1 || 200 || 200 || 0 || 0 || 400 ||
 * 2 || 205 || 195 || .1351 || 10 || 400 ||
 * 3 || 210 || 190 || .4003 || 20 || 400 ||
 * 4 || 215 || 185 || .5458 || 30 || 400 ||
 * 5 || 220 || 180 || .7234 || 40 || 400 ||
 * Mass Difference Held Constant ||
 * Trial || Mass 1 (g) || Mass 2 (g) || Acceleration (m/s^2) || Change in Mass (g) || Total Mass (g) ||
 * 1 || 120 || 100 || .7251 || 20 || 220 ||
 * 2 || 140 || 120 || .5738 || 20 || 260 ||
 * 3 || 160 || 140 || .6069 || 20 || 300 ||
 * 4 || 180 || 160 || .4676 || 20 || 340 ||
 * 5 || 200 || 180 || .4774 || 20 || 380 ||

The following is a graph of Change in Mass vs. Acceleration, which comes from the data in the table labeled “Total Mass Constant”. Based on the strong, positive, correlation between change in mass and acceleration in the graph above, it can be assume that change in mass and acceleration are directly proportional to each other. Also, in this case the linear model adequately fits the data because the correlation coefficient is .9952. Therefore the equation, Acceleration = 0.019(Change in Mass) – 0.01 adequately represents this data set.
 * Analysis**:

The following graph is taken from the data in the table labeled "Mass Difference Held Constant".

There appears to be a negative correlation between total mass and acceleration, which would indicate that total mass and acceleration are inversely proportional to each other when the change in mass is held constant. However, the r^2 value is only .8134, so only 81.34% of the accelerations are explained with respect to the total mass. In order to get a more conclusive graph, more trials would have to be carried out. If the data truly resembled a linear relationship, then the equation would be Acceleration= -.0015(Total Mass) +1.02 Therefore, the equation that could be used when total mass is constantly 400 g to determine acceleration with respect to change in velocity is: Acceleration = 0.019(Change in Mass) – 0.01 The equation to relate total mass and acceleration when the change in mass is constantly 20g would be: Acceleration= -.0015(Total Mass) +1.02 The hypothesis that a greater difference in mass would equate to a greater acceleration was supported by the strong positive correlation of the Change in Mass vs. Acceleration graph, which indicated a direct relationship between the two variables. The hypothesis that no motion would occur when the two masses on the machine were equal was supported by the data recorded in the first table. When the two masses were 200 g and 200 g, the acceleration is equal to zero, and since it started at rest, without acceleration, it must remain at rest. The hypothesis that a greater total mass would not affect the acceleration was not supported by the data. The data showed that there is a negative correlation between the two variables and therefore an inverse relationship. This could be because the higher the mass is on one string, then the acceleration on the other string decreases. If both strings hold large masses, then both accelerations would be decreased, even if they are not decreased by the same amount on both sides. To better improve the data collected in this lab, it would be advisable that I conduct more trials, especially for the data in the second table that did not provide the most conclusive results. Also, it would help to use masses of the same shape to limit the effects of air resistance on the masses that are moving towards the ground. It would also help when it comes to stopping objects from falling out of the cups during their descent.
 * Conclusion:**