Projectile Launch (Kinematics) PDF

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Projectile Launch kinematics This report aims to recognize and exemplify the horizontal position, identify the range in a projectile launch, perform measures of range and height, relate the height of the abandoned metal sphere on the ramp with the range. Using the movement of a projectile, which is subjected to a constant acceleration g, vertical down, there is no horizontal component of acceleration. To carry out the experiment we used a set for moller horizontal launches,a launchpad, sulfite leaf and carbon, releasing a metallic sphere of points 10, 8, 6 and 4 cm and obtaining its range. It was possible to obtain the results in the described positions, when: h=10 its range was 23.8±0.2cm; h=8 its range was 21.9±0.6; h=6 its range was 18.7±0.5 and h=4 its range was 15.2±0.5 showing that the greater the h, the greater the distance reached.

introduction We call the movement of projectiles the free movement of a body launched in a uniform gravitational field, where the acceleration of gravity is constant and vertical, being negligible the resistance of air, as we can observe in Figure I.

Figure II: Projectile launch.

(1)

Where t = time, h = height and g = gravitational acceleration.

Figure I: Theoretical graph range by speed.

Because there is no acceleration in the horizontal direction, the horizontal component Vx of the projectile velocity remains unchanged, maintaining its initial value V0x throughout the movement. Vertical motion is the movement that we can term as free fall and has its constant acceleration. The movement of a projectile is subjected to a constant accelerationg, vertical ly down, and there is no horizontal angleof the acceleration. Based on figure II and the definition of projectile launch until the instant, we can represent the time interval that the projectile is in the air with the equation (1).

Analyzing the vertical movement we can equate with the definition of free fall. The vertical component of the velocity behaves as if it were that of a projectile thrown upwards, and can then be demonstrated in the equation, with this we can say that V0y = 0. (2). (2)

Thus: Where Vy = velocity in component y, g = gravitational acceleration and t = time.

With the analysis of horizontal and vertical movements, it is possible to demonstrate the equations for the module of the initial total velocity at the launch point (V0) and the module of the total velocity at the point where the sphere touches the paper (V), respectively in equations (3) and (4). (3)

Where V0 = initialvelocity , g = gravitational acceleration and h = height.

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ruler was marked the X position0 on the paper that (4)

Where V = speed, Vx² =initial velocity in component x squared, Vy²= velocity in component y squared.

Due to the shape of the sphere and its material, it has the bearing capacity and to calculate this speed we use the equation (5) (5)

The average range measurements are noted along with the + or - signal because of the deviation found. We can take as an example the situation where the radius of the circle, which contains the marks of 5 throws of the metallic sphere, measured 2cm and the average range obtained was 26cm, then the annotation of the measurement of the average range, accompanied by the deviation would be (26±2)cm. This means that the most likely range values are greater than 24 and less than 28cm. Experimental procedure To carry out the experiment, a Moller horizontal launch set (figure III) composed

of: a tripod and three leveling shoes; a launch ramp with positioning scale; adjustable ball support; a metallic sphere; a carbon sheet of paper; a sheet of sulfite paper and an adhesive tape.

Figure III: Moller horizontal release set.

However, the base of the ramp was leveled and then the tripod was positioned marking the shoe so as not to lose its position in case an incident occurs, then one of sulfite and a carbonwas joined on the table, fixed with adhesive tape to not move and using the

is vertically at the exit of the ramp. With the use of a ruler, the height of H wasmeasured, obtaining the value of 23 cm. Following a student handled the steel sphere positioning it on the ramp scale 10 where it acquired speed and made a throw until it collided with the carbon paper marking its position on the sulfite sheet, it was repeated 5 times for greater accuracy. After the measure of scope has been carried out in accordance with Annex I. This process was performed in the scales of 10, 8, 6, 4 of the ramp, such data are shown in table I. Table I: Values of h and Xc. height h (m) 0,1 0,08 0,06 0,04

reach Xc (m) 0.238 ± 0.002 0.219 ± 0.006 0.187 ± 0.005 0.152 ± 0.005

With the data from table I, it was possible to calculate the speed in X and the initial velocity in X, as well as the speeds, with andwithout bearing, for each height where the ball was dropped. Results and discussion With the height data H and taking the value of gravity acceleration as g = 9.8 m/s2 we can calculate the launch time of the sphere through equation 1, this being 0.217 s. From there we calculate the velocity of launching sphere in Y through equation 2, taking V0y= 0 of 2.127 m/s. Using equation 3 and table I data, we calculate the horizontal velocity and the initial horizontal velocity (equation 4) for each of the heights from which the sphere was released, these results are noted in table I. Horizontal speed on the various scales position Vx (m/s) Vo (m/s) Vx1 1,1 1,4 Vx2 1,01 1,252 Vx3 0,9 1,084 Vx4 0,7 0,885 Table I: Horizontal velocity values at the various scales.

To calculate the modular velocity of the sphere we use formula 5, which uses the values of horizontal and vertical velocity, the values can be observed in table II. Modular speed in the various scales position Speed (m/s) 2.39 m/s V1 V2 2.35 m/s V3 2.30 m/s 2.24 m/s V4 Table II: Modular speed in the various scales.

From the analysis of table I, it was observed that the vertical velocity is not modified by the intervention of the horizontal velocity, but as the height that the projectile travels along the ramp increases, it acquires a higher horizontal velocity, consequently reaching a greater range. In addition, the radius of the circle containing the fall markings of the projectile was measured when it touched the sheet and with this it was possible to observe that the smaller the radius, the more accurate the measurements and also greater precision of the launch and range of the projectile. We can observe in Figure IV the data arranged in the tables mentioned above, being possible to trace agrá fico by speed by range and resembles that of Figure I.

Figure IV: Speed graph by range.

With the velocidade frame and considering the rolling motion of the sphere, we can analyze table III. h (m) Vs (m/s) Vc (m/s) % 0,1 1,4 1,18 15 0,08 1,01 1,06 15 0,06 0,9 0,92 15 0,04 0,7 0,748 15 Table III: Values of unrolling and rolling speeds and error percentages. Vs = rolling speed and Vc = rolling speed.

Conclusions

Through this experiment it was possible to conclude that the vertical velocity is not altered by the action of horizontal velocity, but as the height that the metal sphere travels on the ramp increases, thus it acquires a higher horizontal velocity, reaching a greater range and the smaller the scale is the smaller the range....