Laboratory 4_ Projectile Motion

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Southern New Hampshire University *

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193

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Physics

Date

Dec 6, 2023

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5

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Laboratory 4: Projectile Motion PLAB193_08 Prof. David Norwood Abstract :
In this lab, multiple trials were conducted in order to determine if distance over which an object accelerates and the range of the projectile are correlated. This was done so by rolling spheres, of different sizes, with an initial velocity which is set by a 0.8 degree angle of the ramp. The slope of the larger sphere was 1.097x + 1.453 with an R^2 = 0.9704, and the smaller sphere being 0.938 + 1.193 and R^2 = 0.9622. The data shows that the results were consistent and that there is a strong positive correlation between the distance an object accelerates and the range of the projectile. Introduction : In this experimentation hypotheses and tests were conducted on projectile motion. Typically an object will start with zero or no velocity, but in this lab the initial velocity of the two metal spheres is not zero. This was due to the fact that the spheres were on a slightly angled ramp, meaning they did not start with a constant force. The spheres were then rolled down the ramp where they achieved constant acceleration until leaving the ramp and landing onto the floor. Therefore the change in velocity will be in the same direction as acceleration (Δv=vf − v0=at), but the final velocity will not be in the same direction as acceleration (vf =v0+at). This is because final velocity is the addition of two vectors, initial velocity and the change in velocity. Methods : The experiment was set up in a manner so that error would be minimized. The height of the end of the ramp to the floor was 80cm, the angle of the ramp was set at 0.8 degrees, and two spheres of various sizes were used. Multiple trials were conducted at 60cm, 90cm, and 120cm for both spheres, these were considered the distances used (D), x-coordinate. Carbon paper was used to pinpoint the exact location of the point of impact, which was then measured from the distance of the ramp as if it were on the floor; these were considered the range (R ), y-coordinate.
Results : Below are two tables which provide the raw data of all trials and compiled results. Table 1: Big Sphere Starting Distance (cm) Trial 1 (cm) Trial 2 (cm) Trial 3 (cm) Trial 4(cm) Trial 5 (cm) 60 10 10.1 10 10 10.2 90 11.6 11.6 11.5 11.8 11.6 120 13.6 13.8 13.6 13.7 13.3 Table 2: Small Sphere Starting Distance (cm) Trial 1 (cm) Trial 2 (cm) Trial 3 (cm) Trial 4 (cm) Trial 5 (cm) 60 8.2 8.6 8.6 8.7 8.5 90 10 9.7 10.3 10 9.7 120 11.1 11.6 11.6 11.9 11.5
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The graphs show a positive linear correlation. In order to determine whether R , is proportional to the square root of the rolling distance, √D, the following equation is needed, R=√(4 H sin θ) ⋅ D^1/
2. In this equation R is measured as a function of D. D = 60cm = [4 (80cm)(60cm)sin 0.8]^½ = 16.37cm D = 90cm = [4 (80cm)(90cm)sin 0.8]^½ = 20.05cm D = 120cm = [4 (80cm)(120cm)sin 0.8]^½ = 23.15cm Conclusions : In this report, we studied rolling objects with initial velocity in order to determine whether or not there was correlation between the distance over which an object accelerates and the range of the projectile. After completing multiple trials and plotting the data on graphs and using the appropriate equations, it is safe to conclude that there seems to be a strong correlation between the distance over which an object accelerates and the range of the projectile.