EWeaver+Lab+10


 * Lab 10**

The purpose is to find a relationship between differences in masses and the acceleration of the Atwood machine produced.
 * Purpose**

The heavier mass in a pulley will accelerate downward while the lighter mass accelerates upward.
 * Background**

It is hypothesized that as the difference in masses increases, the acceleration will also increase. When the difference in the masses is decreased, the acceleration decreases.
 * Hypothesis**


 * Apparatus**
 * computer
 * 1 Vernier computer interface
 * Logger //Pro//
 * 1 Vernier Photogate with Ultra Pulley
 * 2 mass sets
 * string


 * Preliminary Questions**
 * 1) There would be no motion because the masses are equal, neither mass would accelerate or decelerate.
 * 2) As mass is added to one of the sides, the acceleration would increase. If the mass is increased on both sides the acceleration will gradually increase.
 * 3) For every reaction there is a equal but opposite reaction. So, the mass pulls one side up and the other down

Part 1
 * Procedure**
 * 1) Set up the Atwood's machine with at least 40cm for the mass to hit the ground
 * 2) Connect the Photogate with Super Pulley to DIG/SONIC 1 of the interface
 * 3) Open the file "10 Atwoods Machine" in the provided Logger Pro program. A graph of velocity vs. time will be displayed
 * 4) Put 200g as m2 on one side of the pulley and place 200g as m1 on the other side. Record the data and acceleration.
 * 5) Move 5g from m2 to m1. Record the new masses in the data table.
 * 6) Position m1 as high as possible on the pulley and make sure it's steady. Click "Collect" on Logger Pro and let m1 drop. Catch the falling mass before it hits the floor
 * 7) Click "Examine" in Logger Pro and select a region of the graph where the velocity was increasing at a steady rate. Click Linear Fit and fit the line y= mt+b to the data. Record the slope, acceleration, in the data table.
 * 8) Continue to move masses from m2 to m1 in 5g increments, changing the difference between the masses, but keeping the total constant. Repeat 6-7 for each mass combination, repeat for five combinations.

Part 2
 * 1) Do steps 1-3 of Part 1.
 * 2) Put 120g on m1 and 100g on m2.
 * 3) Repeat steps 6-7 of Part 1 to collect data and determine the acceleration.
 * 4) Add 20g increments to both sides, keeping a constant difference of 20 grams. Record the resulting mass for each combination in the data table. Repeat steps 6-7 for each combination, repeat for five different combinations.


 * Data**

**(g)** ||= **m1** **(g)** ||= **Acceleration** **(m/s2)** ||= **Δm** **(g)** ||= **mT** **(g)** ||
 * = **Table 1: Part 1 – Total Mass Constant** ||
 * = **Trial** ||= **m1**
 * = 1 ||= 202 ||= 200 ||= 0 ||= 2 ||= 402 ||
 * = 2 ||= 207 ||= 195 ||= 0.1771 ||= 12 ||= 402 ||
 * = 3 ||= 212 ||= 190 ||= 0.3811 ||= 22 ||= 402 ||
 * = 4 ||= 217 ||= 184 ||= 0.6281 ||= 32 ||= 401 ||
 * = 5 ||= 222 ||= 180 ||= 0.8297 ||= 42 ||= 402 ||

**(g)** || **m1** **(g)** || **Acceleration** **(m/s2)** || **Δm** **(g)** || **mT** **(g)** ||
 * **Table 2: Part 2 – The Mass Difference Constant** ||
 * **Trial** || **m1**
 * 1 || 120 || 100 || 0.6538 || 20 || 220 ||
 * 2 || 140 || 120 || 0.5922 || 20 || 260 ||
 * 3 || 160 || 140 || 0.4111 || 20 || 300 ||
 * 4 || 180 || 160 || 0.3829 || 20 || 340 ||
 * 5 || 200 || 180 || 0.3487 || 20 || 380 ||


 * Analysis**

3.) The Acceleration // vs. // Time Difference graph shows that the relationship is linear. The line of bet fits reveals that the equation of the line is about y=.021x-.61. The acceleration is increasing constantly as the difference between the masses increases.

4.) The graph of Total mass (X) vs. Acceleration (Y) shows is linear with a line of best fit, y= -.002x to 1.092. As the total mass increases, the acceleration decreases.

A better fit for the Total mass vs. Acceleration would be a quadratic fit which results in a close fitting quadratic equation, y = -7E-09x 4 + 9E-06x 3 - 0.003x 2 + 0.759x - 54.27

5.) If a = 0.021(mass difference) - 0.061 and a = -0.002(total mass) + 1.092, then when the vectors are combined, 2a = 0.021(mass difference) - 0.002(total mass) + 1.031 . a = 0.0105(mass difference) - 0.001(total mass) + 0.5155.

If we were to use y = -7E-09x 4 + 9E-06x 3 - 0.003x 2 + 0.759x - 54.27 the combined equation would be  2a = 0.021(mass difference) - 7E-09 (total mass)4 + 9E-06(total mass)3 - 0.003(total mass)2 + 0.759(total mass) - 54.331. a = 0.0105(mass difference) - 3.5E-09(total mass)4 + 5E-06(total mass)3 - 0.0015(total mass)2 + 0.3795(total mass) - 27.1655.


 * Conclusion**

In conclusion, the hypothesis for the lab was proved to accurate from the data collected. The graph shows that as the difference in masses increases the acceleration will also increase. After analyzing graph 1 we can conclude that it is from the equation F = ma. The net force increases as the mass increases. Part 1 of the experiment shows that as m1 gets bigger and m2 gets smaller, the same amount, the force gets larger. In Part 2, a linear mode does not represent the data well. The data is better represented by a quadratic. However, it can be seen that as the total mass, the acceleration decreases. The data in Part 1 is more accurate than Part 2, but both parts fairly represent what they are meant to.