Gravity

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Jan 9, 2024

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General Physics I Laboratory (PHY221L) Gravity Name: Aliyah Zito Date: 09 / 19 / 2023 ______________________________________________________________________________ Introduction State what you show or demonstrate in this laboratory experiment. Include the background/theory and any useful equations used in the lab. (5 points) (3-5 sentences) This experiment demonstrates the time it takes for a rubber ball to free fall from a table surface to the ground. You will also use a virtual lab to demonstrate how many seconds it takes for the ball to shoot out of the cannon at specific heights. Method Part 1: Free Fall for rubber ball 1. 1. Write the precisions of your measurement tools (i.e. ruler). (2 points) Ruler : 1mm Phone stopwatch: 0.1 s 2. Measure the height from tabletop to the ground and record in Table 1 3. Drop the rubber ball off the edge of the table, and record the time it takes for the ball to strike the floor. 4. Repeat this for 10 times and record the free fall times in Table 1. 5. Using the equation below find the value for gravitational acceleration g for each time value recorded. Refer to the introduction document for more information. h = 1 2 gt 2 Part 2: Free fall at different heights (Using PheT Interactive Simulation) To verify the objective of this part using phet interactive simulation, do the following: 1- Open the following link: https://phet.colorado.edu/sims/html/projectile-motion/latest/projectile-motion_en.html 2- From the home page of this link, click on lab, from lab window use the provided controllers to adjust the height (h) and the velocity of the launched ball, the mass, the objects shape (see the Figure below). Adjust the first height at 14m and the velocity must be at zero (Free Fall). Release the ball and use the time meter (control the time meter and fix it at the final point of the ball) to measure the time needed for the ball to travel 14m in vertical direction. Record your data in table 2. 3- Change the height (h) to 13m, release the ball and measure the time needed to travel 13m in the vertical direction. Record the new values in table 1.

4- Repeat step 3 to fill table 1. 5- Calculate the ½ t 2 for each time value and record in Table 2. Results (48 points) Place your data in this section Table 1: Free fall for rubber ball Height - h (m) Time- t (s) g (m/s 2 ) 79.5 cm 0.795m 0.45 7.85 0.41 9.46 0.46 7.51 0.44 8.21 2 You can control the height (h) by clicking on the + sign on the canon and then move it up or down to change y. Time meter, click on the +sign and drag it to the final point Velocity controller Final point of the ball

0.43 8.60 0.42 9.01 0.45 7.85 0.41 9.46 0.38 11.01 0.43 8.60 Table 2: Free fall at different heights Height - h (m) Time- t (s) ½ t 2 (s 2 ) 14 1.69 1.43 13 1.63 1.33 12 1.56 1.22 11 1.5 1.13 10 1.43 1.02 9 1.35 0.91 8 1.28 0.82 7 1.19 0.71 6 1.11 0.62 5 1.01 0.51 Data Analysis (30 points) This part is for data analysis. You can insert graphs and a sample of your calculation. 1. Find the average gravitational acceleration for g for Table 1. (5 points) =8.75 3

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2. Using EXCEL, plot height (h) versus time-square (½ t 2 ) for table 2. Apply linear trend line ( y ( x ) = Ax ) and include its equation and R-square value in the plot. Insert the graph below. Remember to include graph title, axes titles along with units, trend line, trend line equation and R-square value on the graph (10 points) 3. Using the trend line equation obtained above, find the gravitational acceleration. (5 points) Hint: Compare trend line equation ( y ( x ) = Ax ) with h = 1 2 gt 2 and determine the value of g (gravitational acceleration). [ A = g ] 4

Trend line equation: Y=9.7953x-0.0014 G=9.7953 4. The true value of the gravitational acceleration is 9.8 m/s 2 . Compare between the true and experimental value (as in question 1 & 3 above) of the gravitational acceleration by calculating the percent errors for each. (10 points) %error=(est #-actual#)/100% =10% Conclusion (15 points) State the main conclusion(s) in the first paragraph along with a discussion of your results. In conclusion are results had very low error, our percent error was 10%. The time recorded was pretty much constant with little diversity. In the second paragraph, you must show once how your measuring tools produce a quantified experimental error and discuss its implications for your results. 5

We used our cell phone stop watches in this experiment. Some errors that occurred within the experiment included reaction time in stopping the timer. We found that some stopped the timer faster than others which produced different data. In the third paragraph, you may discuss any other experimental errors qualitatively that may have influenced your results. Some other errors may include someone not dropping the ball in the same exact position and height every time. 6

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