Lab 3 - Projectile Motion.docx

Lab 3 - Projectile Motion.docx - Mackenzie Corbin Shannon...

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Mackenzie Corbin Shannon Hawkins Projectile Motion Abstract Using a projectile launcher with a wide variety of combinations of launcher strengths and angles, , we ϴ test the relation between the initial speed and the angle from which the projectile was shot, based on Galileo’s law of free fall. This law implies that the (gravitational) acceleration g , of a body in free fall is downward and the acceleration at which it falls to the ground is constant. We roughly verified this prediction by experimentally obtaining a linear range versus s , or sin2 ϴ g graph. The equation derived from Galileo’s law of free fall is R = V ˳ 2 g sin 2 ɵ . The equation derived from the principles of kinetics is V ˳ = 2 gh . Also, by comparing the slope of the graph by the theoretical relation between the range and s , we found that the V 0 2 (short range) = (7.9749 ± 0.2786) m/s 2 , V 0 2 (medium range) = (19.877 ± 1.083) m/s 2 , and V 0 2 (long range) = (35.274 ± 2.955) m/s 2 . Theory According to Galileo’s law of free fall, the (gravitational) acceleration g of a body in free fall is downward and the acceleration at which it falls to the ground is constant. Assuming the path of the projectile follows Galileo’s laws, the following equations are used to solve for initial velocity (See Fig. 1). The range of the projectile is represented R , while g , the gravitational acceleration is measured at -9.8 m/s 2 , R = V ˳ 2 g sin2 (1). In the equation ϴ is the various angles at which the ball was flung ϴ by the projectile launcher. Derived from the V y 2 = V 0 2 -2gh equation of kinematics, to find the velocity at maximum height, V˳ = 2 gh (2). The model for maximum height is represented in figure 2. Procedure Figure 2: Model of Upward Motion Figure 1: Model of Projectile Motion ɵ
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We alter the axis position and spring tension of the projectile launcher (Fig. 2) from its initial angle and strength to determine the range of the ball at different launch angles and launcher strengths. We measure the range X of the ball with the launcher loaded at “short range” for each of 5 different angles using carbon paper and a meter stick (Fig. 3). We find X ± R for each angle, where the uncertainty R is mostly due to a combination of error in the experimental precision of the meter stick and some human error while using the apparatus or measuring range. We run the same procedure
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