Comparison of Experimental Results for Projectile Motion in Two Dimensions - Lab Report Example

Parabolic movement is the path traced by an object vertically, with constant acceleration, while the movement horizontally is at a constant velocity. The initial velocity and the projection angle determine the range. The initial angle’s complementary values result in the same range but the heights are different. 45o is the projection angle with the maximum range.

Apparatus Meter sticks A spring-loaded gun Procedure For the Gun calibration:1. The spring gun was set up and levelled.2. A mark perpendicular to the release point of the projectile was put on the floor3. The height of the projectile (Δy) was determined.4. A sheet of paper was fixed with a sheet of carbon on its top where the projectile was most likely to land.5. The gun was loaded and fired, and the range (Δx) measured.6. The experiment was repeated five times and the average was calculated.7.

The initial velocity of the gun was calculated.Δx = v0x t; and since we do not know vox and accurate measurement of time is difficult, Δy = v0y t + ½ a t2v0y = 0Δy = ½ a t2t = √-2Δy/vox = vg = Δx / t Therefovoxvoxv0 = Δx/tf tf = (-2Δy/g)½ To determining the range:1. The spring gun was set up at an assigned angle.2. The range per each angle was calculated. The gun was not fired until the range was found.3. The gun was loaded, fired and the range measured.4. The experiment was repeated three times, and the average of the range was taken.5. The whole procedure was repeated for the other angles.

For this experiment, the velocity is still constant in the x-direction (vox = vx = constant). The only difference is that the velocity has a y-component (vo = (vox2 + voy2)½ ). For both experiments, the initial velocity is the same (vox = vo cos q and voy = vo sin q). To find the motion’s equation, Δy = v0y t + ½ a t2, t was solved: ½ gt2 + vo sin q t – Δy = 0Δx was calculated: Δx = vo cos q tThe quadratic Equation: t = (-b +/- (b2-4ac)½)/(2a)Part 1For both experiments, the height of the projectile is the same.

Tathe ble 1: Average range and initial velocityHeight Time Velocity 1.20 m 38s6.87 m/ sTable 2:Number Δx (m)Average (m)Time Velocity( m/ s)12.54 m2.6106 m0.494 s5.28 m/ s22.632 m32.653 m42.557 m52.675Part 2Table 3: Distances per assigned anglesAngle 300400 450600Horizontal dist 12.652.872.822.21Horizontal dist 22.632.902.782.25Horizontal dist 32.612.892.862.24Average distance2.632.882.822.23Total distance2.632.882.822.23Calculated L4.6524.2593.822.616Percent error78.20%63%46.32%0.21%Figure 1: Plot of Angle against Average range Discussion There is a significant difference between the theoretical range and the experimental range.

Errors could have occurred due to incorrect readings because of parallax and calculation errors because of rounding off. Conclusion These experiments, despite having quite evident errors, the angles with the highest range are 400 and 450. The experiment further emphasized the independence of x- and y-components in projectile motion (Serway, Vuille & Faughn, 65).