PHY 211 - Lab 7 Worksheet-2

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Researcher: Catherine Goodman Data Analyst: Lily-Kate Hubbs Principal Investigator: Jada Lunsford DA: Lily-Kate Hubbs PI: Jada Lunsford Researcher: Catherine Goodman Lab 7: Momentum Worksheet 1) Researcher(R1): The researcher is responsible for explaining the above steps in detail. Special attention should be given each time mass is used in a formula to make it clear whether the mass is referring to “the mass of the ball”, “the mass of the pendulum” or “the mass of both.” The first thing we did for this lab was find the mass of the ball that we were going to use for the experiment. To do so, we just used the scale provided for us. Our next step was to find the mass of the pendulum using a scale. Then we were able to measure the center of mass for the pendulum by meticulously balancing it on the edge of the ruler provided for us. Using the distance from the small hole in the middle of the pendulum to the center of mass in order to get the radius of the pendulum. We then secured the pendulum and ball launcher to the edge of our lab station. We used the tape measurer to measure the height from the floor to the pendulum. Then using the iron stand and a piece of blank white printer paper as a marker, we predicted where the ball would land using the equation. Before we launched the ball, we found the angle for the zero offset of the pendulum on the angle measurer. After all these steps were completed, we loaded the ball into the launcher and shot it in the direction of our predicted location. Once the ball landed, we used the tape measurer to measure the actual distance of where the ball landed. 2) Researcher(R2): Explain with equations, how the measurements of height and angle of the projectile launcher produced the final result, the predicted distance traveled. The first equation we used the angle that the pendulum marked for us after the ball was launched. We then had to measure the change in height of the pendulum after the ball was launched and the equation used was: ∆ 𝐻 = 𝑅 ( 1 − ???𝜃 ) Then using the change in height that was found from the previous step, we could then find the change in potential energy of the system. The quation for change in potential energy uses mass, gravity and height. So, the official formula of this is: ∆ 𝑃𝐸 = ?𝑔 h

Researcher: Catherine Goodman Data Analyst: Lily-Kate Hubbs Principal Investigator: Jada Lunsford Then, using this equation and the answer from it, we were able to find the change in the Kinetic energy in the system. We know that according to the Law of Conservation of Energy, the change in potential energy and change in kinetic energy will be the same answer. We were then able to solve for the momentum of the pendulum knowing this information. The equation for this is: ? = √𝐾 𝐸 × 2(????? + ?????????) Then you can use this information to find the initial velocity of the system using the conservation of momentum. Then you can take the answer from this to find the velocity of the ball using the equation: ? = ?? Once you have this answer, you can use the following equation to find the predicted distance of where the ball will land: ∆𝑥 = 1 2 ?? 2 +v o t 3) Researcher(R3): the DA will provide some form of graph that shows the “random uncertainty” from the projectile launcher. However, the group introduced some “systematic uncertainty” based on how they made the measurements of masses, angles, and radius of the pendulum. In your personal copy of the excel data adjust the values referenced by the equations to see which of the measurements have the greatest impact on the “predicted distances.” We are looking for statements like “The .5 (unit) uncertainty in XXX caused our predicted distance to change by about # ?? . This (does/doesn’t) account for the differences between our predicted distances and the actual distances. What is the single largest source of uncertainty in your final results. Is this a “systematic uncertainty” or a “random uncertainty?” Using the information below, you can see that there is a 0.0005 kg uncertainty in the mass of our ball. This information tells us that our predicted distance could change by about us that that our predicted distance could change by about 0.5cm. You can see that our predicted values and actual values were relatively not very close. Our predicted distance was a bit shorter compared to the predicted. One source of uncertainty could be air resistance and there may have been human error in the setup of our system. 4) DA1: Include the entire raw data table for only one of the balls as well as the information at the top that was used in all trials.

Researcher: Catherine Goodman Data Analyst: Lily-Kate Hubbs Principal Investigator: Jada Lunsford 5) DA2: Decide on a simple graphical method to represent the predicted distance and actual distance for all of your data. Thirty points on a graph will be difficult to understand so make sure that you consolidate your data and take advantage of error bars to make the reader able to understand your data easily. 6) DA3: Create a caption for your Chart which explains in words what the graph means about your experiment. Mention the “single largest source of uncertainty” identified by the Researcher (in R3 above) and how that is integrated into the graph (or how it would adjust the graph if it is not yet a part of the graph). The chart above shows the average predicted and actual distance each ball traveled to the target piece of paper. According to our graph, the actual distance was larger than our predicted

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Researcher: Catherine Goodman Data Analyst: Lily-Kate Hubbs Principal Investigator: Jada Lunsford value. The single largest source of uncertainty is demonstrated in our graph through error bars as it shows the variations between measurements. 7) PI1: Your ultimate goal is to address whether conservation of momentum and conservation of energy allowed the group to make accurate predictions of distance that the ball travelled. Make sure you use the graph(s) presented by DA to make your argument. Conservation of momentum and conservation of energy did not allow the group to make accurate predictions of the distance that the ball traveled. We can tell from the graph because for two out of three of the balls, the error bars do not overlap. 8) PI: Evaluate the graphs for each ball generated for DA2 while considering the largest uncertainty identified by the researcher R2 in Step 24. Our graph indicates that our predicted data was not calculated correctly and was extremely shorter than our actual data. A lot of our errors could be contributed to the large uncertainty identified earlier. 9) PI3: Summarize: Did your group successfully determine the actual and the predicted distances for each of the three balls? How well does the actual and predicted distance compare? Our group did not successfully determine the actual and the predicted distances for each of the three balls as they were not close in numbers. The actual and predicted distances are not close at all. Our uncertainty was 0.005 k, and the difference between the actual and predicted exceeded that number.

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