physics 6AL lab one-2

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Ella Nouhi Williams Lab 1 phys 6AL prelab: Exercise 1: In space (no gravity), at t=0 s t =0 s, a ball is shot towards a wall at a velocity of 7.5 m/s. The ball hits the wall and perfectly reflects after collision, maintaining the same speed . At t=4 s , the ball is measured to be 20 m from the wall. a. Did any forces act on the ball? Defend your answer, explicitly referencing the ball's initial and final velocities as needed. Yes, the wall exerted a force on the ball which was required to change its direction, and thus its velocity. If going in the opposite direction at the same speed, final velocity is -7.5. Since final velocity does not equal initial velocity, a force must have acted on it. b. How far was the ball from the wall initially? The ball traveled a distance of x in 4 seconds, always traveling at 7.5 m/s (though changing direction at one point), so x = 7.5x4 = 30. The initial position is 30-20 = 10m c. Sketch a graph of the ball's distance from the wall over time. You can do this on a digital drawing program or on paper and take a picture to attach to your report. Exercise 2 A. y(t)=½(a)t^2 + v 0 t + y 0 a. 0 m= ½(-9.81 m/s)(t)^2 + (5 m/s)(t) + 0 0 = -4.905t^2 + 5t 0=t(-4.905t + 5) 0=t; 0=-4.905t+5 -5=-4.905t t= 5/4.905 t=1.02 s B. Highest point: velocity=0 v ( t )= at + v0 0 = -9.8m/s(t) + 5m/s t=0.51 C. y(t)=½(a)t^2 + v 0 t + y 0 Ymax = ½(-9.8)(0.51)^2 + 5(0.51) + 0 = 1.27 m

Exercise 3 A. y 0 = ½(-9.81 m/s)(tf)^2 + (0 m/s)(tf) y 0 = -4.905(tf)^2 (tf)^2= y 0 /4.905 tf=√y 0 /4.905 B. Initial heights: y 0 =1.0 m i. tf=√1.0/4.905= 0.45 s y 0 = 5.0 m ii. tf=√5.0/4.905= 1.01 s y 0 = 20.0 m iii. tf=√20/4.905= 2.02 s y 0 = 50.0 m tf=√50.0/4.905= 3.19 s y 0 = 0.0 m iv. tf=√0.4.905= 0.0 s C. Exercise 4: 1. A wind causing horizontal acceleration would cause the ball to take a longer, diagonal path, which would take longer, increasing tf.

2. Human error in usage of the stop watch could render it less precise, which would skew the final values. Depending on the error, this could increase or reduce the final time. 3. Another factor that could affect the accuracy is that we use a calculated constant, g, to describe gravity, and that may not always be 100% accurate. The actual gravity acting on the ball may be slightly varied from the constant used, which could increase or decrease the time it takes for the ball to fall. Exercise 5: Floor 2: 5.75m ± 0. 1𝑚 Floor 3: 9.37m 0.1m ± Floor 4: 13.0 m 0.1m ± Exercise 6: link to data: (we pasted with link, but it does not seem to be working) https://docs.google.com/spreadsheets/d/1nBsVkOyZkl6L8zwY9LRfgjZNkYi7hmAdWPNJ wkdBQR0/edit?usp=sharing Table 1: Ball 1 Drop Height (m) Theoretical tf (sec) Object 1 Avg. Measured tf (sec) Object 1 Percent Difference Measured Average Velocity (m/s) 5.75 1.08 1.08 0.377 5.33 9.37 1.38 1.05 27.1 8.90 13.0 1.63 1.28 23.8 10.1 Table 2: Ball 2 Drop Height (m) Theoretical tf (sec) Object 1 Avg. Measured tf (sec) Object 1 Percent Difference Measured Average Velocity (m/s) 5.75 1.08 1.00 8.04 5.76 9.37 1.38 1.24 10.8 7.56 13.0 1.63 1.60 1.67 8.12

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Table 3: Ball 3 Drop Height (m) Theoretical tf (sec) Object 1 Avg. Measured tf (sec) Object 1 Percent Difference Measured Average Velocity (m/s) 5.75 1.08 1.25 14.1 4.61 9.37 1.38 1.86 29.3 5.05 13.0 1.63 2.46 40.8 5.28

Exercise 7:

a. Which of the objects most closely follow the theoretically predicted drop time? Object 2 most closely followed the theoretically predicted drop time as the average percent difference was the lowest for object 2. b. Which of the objects have the greatest percent difference with the theoretically predicted drop time? The greatest percent difference with the theoretically predicted drop time was seen in Object 3. c. For the object in part (b), is the percent difference greater for higher or lower drop heights? The percent difference is greater for higher drop heights. Exercise 8: a. Does the plot look linear? Why or why not? Yes, very linear, r^2 = 1. This means that the velocity stayed relatively constant over all three trials. b. What is the slope of the line of best fit, including units? The slope of the line of best fit is 0.168 m/s. c. What is the physical meaning of the line of best fit? The slope of this line is the velocity in m/s. Exercise 9: a. How do the average velocities from different fall distances compare to one another? Elaborate on if you see a trend. The average velocities increase as the drop height increases. We believe this is because of acceleration due to gravity acting on the ball for a longer amount of time.

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b. Make an educated guess as to what the average velocity of this object would be if you dropped it from a height of 500 m, and support your hypothesis with your data . Exercise 10 a. Which objects, according to your data, were most influenced by air resistance as discussed? Support your conclusion with a sentence or two. Object 3 was most influenced by air resistance as seen in our data as well as when conducting the experiment. The data for object three had the highest percent difference in comparison to the theoretical data. Furthermore, we could see this visually as object three was being heavily swayed by the wind. b. Does it make sense to you that these mentioned objects were affected most by air resistance? What physical properties do they have that might lead to high air resistance? Yes, it does as this is the object with the least mass rendering it most susceptible to air resistance affecting its path as it drops. Exercise 11: a. Do you think that the uncertainty introduced by you and your classmates' reaction times is significant in this experiment? Please answer this quantitatively, referencing your measured reaction time from this Exercise in Lab 0 and comparing it to the variance in measured times. The uncertainty introduced by my classmates and I was significant in this experiment as the reaction time in Lab 0 had an average of 220 ms or 0.22 seconds. This is significant for our experiment, as our data is measured in seconds. Some of our times are around 1 second, and this means the reaction time is 22% of that time. This is a significant portion. Variance between classmates was upwards of 0.1 seconds, in the same range. You all had to start a stopwatch on a certain agreed upon signal, and then stop it the instant an object hit the ground. Do you think that the systematic errors associated with the average delay in reaction time resulted in a bias in the measured being longer? I think that people may have been trying to compensate for their reaction time by stopping the stopwatch early because a lot of the measured times are actually less than

the theoretical times, especially for object 1. For object three the measured is much longer than the theoretical, which may be due to reaction time, or due to the fact that it was extremely windy which caused the drop time to be much longer. For example, the ball took a longer path as a result of the wind as seen when it hit a bush during the drop which is why we see this for object three while we see the opposite effect for object one and two. b. Do you think that there any environmental factors that could have significantly altered the results of the experiment? . Argue your answer in a sentence or two. Pointing to evidence in the data is strongly encouraged for full credit. For object three, we had percent difference of up to 40.8% at the highest drop height, indicating that some factor was altering our results. We noted wind in the area at the time of the experiment, which likely increased the time it took the ball to drop by lengthening its path diagonally. Exercise 12: In this experiment, three different objects were dropped from varying heights and the drop time was recorded; these measured times were then compared to the theoretical drop times calculated using the equation below: Theoretical Drop Time =sqrt((2*Drop Height)/9.81 m/s^2) Average times from the class were recorded, and percent difference between measured and theoretical times was calculated. Based on this experiment, the laws of linear motion do not function ideally in nature. While our percent error for some points was as small as 0%, there were others where measured time differed from the calculated time (using the linear relationship expected) by 40.8%. This shows that there are clearly factors that cause behavior to stray from expected linear relationships. One thing we noted when completing this experiment that may have altered this relationship was the fact that it was windy outside. We could feel the gusts of wind and saw the beach ball (object 3) moving horizontally as it fell. Furthermore, the beach ball even would hit the bushes around before hitting the ground which further altered our data. We had a wide range of percent differences, leading us to conclude that for smaller, denser objects these linear relationships hold more true than for larger objects with less mass.

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