Lab3

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Mark Acosta - Feb 9, 2024 Experiment 3: : Atwood’s Machine’s In this experiment, I analyzed the relationship between friction, mass, and acceleration. By connecting two weights by a string that runs along two pulleys, I was able to visualize the Newton’s 2nd law of motion. By changing the weight on one side of the pulley, there was changes in acceleration, resulting in changes in the time of motion. Procedure For the procedure, I used an atwood machine that consisted of a double pulley, an attached meter stick, and a clamp. To perform the experiment, I used two 100g weights, 2 10g weight, a 20g weight, 40 g weight, and a 50g weight, along with a stopwatch. I began by setting one of the 1kg weight on the floor, by doing this, the other 1kg weight was at a height of 1.5 m above the ground.

This image shows the initial setup:

To find the mass of the friction Mf, I added mass onto the weight above ground until there was slow motion that stopped halfway through. This happened to be 0.01 kg. Shown below is the setup with Mf now integrated into the pulley: For every additional mass, m3, I simply added 0.01 kg onto the system with Mf implemented. For example, below is the set up for the first mass (0.01kg) m3. Since Mf is 0.01 kg and m3 is .01 kg, I used a .02 kg weight.

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I then recorded the time it took the weight to reach the floor 5 times, and my lab partner recorded the time 5 more times, for a total of 10 times. We then repeated this process for m3 = 0.02kg, 0.03 kg, 0.04 kg, 0.05 kg, 0.06 kg, and 0.10 kg.

A) For each value of M3 that you used, calculate the average time t for the weights to fall and the standard deviation t in the time. Then calculate the experimental acceleration a from Eqn. (III-3) To calculate the the average time and standard deviation for each m3, I inserted by data into excel, using the ‘=AVERAGE( )’ and ‘= STDEVA ( )’ functions in the program. Below is my recorded time as a function of m3. Note the data is divided into two tables for better visibility:

Plot your acceleration values (complete with error bars to indicate the level of uncertainty) as a function of M3. According to Eqn. (III-5), this curve should have a zero intercept. Further, since M3 « MA + MB , the curve should be (approximately) a straight line with an initial slope of g / (MA + MB + MF) . Does your plot look like this, or is there a nonzero intercept? If so, what is the meaning of this intercept? My curve is approximately a straight line, but there is a nonzero intercept and the inital slope is To plot my experimental acceleration values as a function of M3, I first calculated acceleration, shown below:

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I then plotted the values as a function of m3 in excel, which gave me the following graph:

Furthermore, I calculated the retarding force (Fr) for each additional mass (m3): Since one of the weights (Mb) had additional mass, it can be assumed that Mb = Mb + M3 + Mf.

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Compare your experimental results with predictions based upon Eqn. (III-5). Plot the predicted values on the same graph. To compare my values with the expected values, first solved for acceleration for each m3, shown below:

I then inserted these values into the m3 vs experimental a data, giving me the following graph: As you can see, the results are quite similar, with error in the acceleration. These errors are likely due to human error when taking measurements of time. For example, stopping the time too early or too late. Finally, note that the prediction you just checked depends upon the acceleration of gravity. This implies that we could turn the question around and use this experiment to measure g. What value does your data today give for g? For g, the data gives us the slope, so moving the equation: slope = g / (2Ma + M3 + MF) we get the equation: g = slope / (2Ma + M3 + MF). This gives an estimated gravitational acceleration of g = 9.5 m/s^2. The reason for this error is also due to the fact that measured times are not

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accurate when conducted by the naked eye. To reach a more appropriate estimation for gravity, more advanced time measuring tools can be used, completely removing human error.

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