Lab 4- Projectile Motion

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Arizona State University *

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Physics

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Oct 30, 2023

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Lab 4: Projectile Motion 1. Testable Question: How does the horizontal position of the ball relate to the vertical position/ height? 2. Hypothesis: If the horizontal position increases, the vertical position will also increase because, as the projectile has more time in the air, it has more time for gravity to pull it down. 3. Variables: Control(s): Initial velocity (V 0 ), Launch Angle ( q ), Diameter of Projectile (d), Initial Position (X 0 ) Independent: Horizontal Position (X) Dependent: Height/ vertical position (Y) 4. Experimental Design: V 0, X 0, q , d i V 0 (m/s) X (cm) Y (cm) 1–8 V1 X1-8 Y1-8 1–8 V2 X1-8 Y1-8 5. Materials: Wood board Plum bob Projectile Spark XLi Safety glasses Photogate C-clamp Meter stick Carbon paper Tape Paper towel Level
6. Procedure: Setup: 1. Set up as shown above 2. Gather the starting height as the start position in both the x and y direction 3. Downward measurements are made positive in this lab 4. Before launching, make sure the shot is fired with the same initial speed (either 1 or 2 notches). To gather the origin, place the wood board directly in front of the launcher. Mark points with the corresponding values, so data does not get confused. 5. Measure the horizontal values with the meter stick along the floor. Then place the wood bord in the corresponding position to represent the y values. 6. Collect the independent data values for each launch to gather the speed of projectile as it exits the launcher. 7. Set the Spark XLi to velocity and place between the gates. Be sure to have the proper distance measured to obtain the desired speed. Launch at the same horizontal distance 3 times and average those measurements to gather the average speed. The averages will be used to solve for theoretical slope. 8. Starting at 20 cm on the horizontal launch the ball at a slow speed for 8 intervals increasing by 20 cm. 9. Mark on the carbon paper where the ball has made a mark 10. Gather measurements of each mark compared to the initial mark made for setting the origin. 11. Repeat the following steps at a higher speed.
12. TS: a v 2 0 2 7. Data: q =0 d=@2.55cm x 0 =0.00 cm V0= 475 cm/s V0= 743 cm/s x (cm) x2(cm2) y (cm) y (cm) 0 0 0 0 20 400 0.735 0.433 40 1600 4.42 2.27 60 3600 10.4 3.40 80 6400 15.5 6.17 100 10000 24.3 10.7 120 14400 35.8 14.4 140 19600 50.5 19.2 8. Data Analysis: 0 20 40 60 80 100 120 140 160 0 10 20 30 40 50 60 x (cm) vs y (cm) slow speed medium speed y (cm) x (cm)
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0 5000 10000 15000 20000 25000 0 10 20 30 40 50 60 f(x) = 0 x R² = 1 f(x) = 0 x R² = 1 y vs x^2 475 cm/s- short range Linear (475 cm/s- short range ) 743 cm/s- medium range Linear (743 cm/s- medium range ) x^2 (cm^2) y (cm) Short range: TS= a v 0 2 2 TS= 9 . 81 475 s 2 2 TS= 0.00217 cm/s MS= 0.00250 % error = | 0.00217 0.00250 | 0.00217 × 100 % error = 15.2% Medium range: TS= a v 0 2 2 TS= 9 . 81 743 s 2 2 TS=0.000889 cm/s
MS= 0.00100 % error = | 0.000889 0.00100 | 0.000889 × 100 % error = 12.4% Vertical Position: D y= v 0 t + 1 2 at 2 D y= 1 2 at 2 t = D y 2 a Horizontal Position: D x= v 0 t + 1 2 at 2 D x= v 0 t t = D x v 0 9. Conclusion: The height/ vertical position is directly proportional to the square of the balls horizontal position, according to: (Short Range) y = 0.00250x ^2 cm (Medium Range) y = 0.00100x^2 cm As the position of the ball changed horizontally, the balls vertical position also showed an increase because, the projectile had longer airtime allowing gravity to pull it further down. Looking at the graphed data, the slow and medium range present different slopes. This is because the ball shot at the short range had a longer period to fall due to gravity. 10. Evaluation:
The hypothesis was supported because, when the horizontal distance increased, the vertical distance increased as well due to the pull of gravity on the projectile. During this lab, the level of accuracy is fair with a with a percent error resulting in 15.2% as well as 12.4%. For both values (short and medium range) the MS presented a higher value than the TS. A systematic error that could’ve occurred for the inaccuracy in data could be that the Spark XLi gathered data at a different point than the initial crossing of the projectile, resulting in a higher value. The level of precision presented during this lab showed an outstanding result. The R2 value of the short range being 0.999 and the R2 value for the medium range being 0.9984. A random error that may have occurred to show this slight imprecision could have been fluctuations in measuring the measured data points to the initial starting line.
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