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It is the superposition of two independent motions in x- and y-directions. The motion in the x-direction is uniform meaning that there is no…
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Physics lab report Purpose The aim of this experiment is to compare experimental results for projectile motion in two dimensions, using a meter stick and a spring-loaded gun, with theoretical calculations.
Introduction
Projectile motion is the motion experienced by an object in two dimensions due to its attraction of the earth, air friction ignored. It is the superposition of two independent motions in x- and y-directions. The motion in the x-direction is uniform meaning that there is no acceleration since the velocity is constant (Serway, Vuille & Faughn, 65).
ax = 0.
vx= v0x
x = vxt.
The motion in the y-direction is a free fall.
ay = - g vy = – gt
Dy = - ½ g t2
Since the velocity = 0 ( voy = 0), the gravity acceleration (g) = +9.81 m/s2
The 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 stick
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 floor
3. 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 t2
v0y = 0
Δy = ½ a t2
t = √-2Δy/g
vox = vg = Δx / t
Therefore, v0 = 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 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 = 0
Δx was calculated: Δx = vo cos q t
The quadratic Equation: t = (-b +/- (b2-4ac)½)/(2a)
Part 1
For both experiments, the height of projectile is the same.
Table 1: average range and initial velocity
Height
Time
Velocity
1.20 m
38s
6.87 m/ s
Table 2:
Number
Δx (m)
Average (m)
Time
Velocity( m/ s)
1
2.54 m
2.6106 m
0.494 s
5.28 m/ s
2
2.632 m
3
2.653 m
4
2.557 m
5
2.675
Part 2
Table 3: Distances per assigned angles
Angle
300
400
450
600
Horizontal dist 1
2.65
2.87
2.82
2.21
Horizontal dist 2
2.63
2.90
2.78
2.25
Horizontal dist 3
2.61
2.89
2.86
2.24
Average distance
2.63
2.88
2.82
2.23
Total distance
2.63
2.88
2.82
2.23
Calculated L
4.652
4.259
3.82
2.616
Percent error
78.20%
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).
Work cited
Serway, Raymond, A. & Jerry, S. Faughn. College Physics. Fort Worth: Saunders College Publisher, 2014. Print Read More
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