Physics 195Oliver Gorton Darrione, Jose, David, Kate Lab 5: Projectile Motion 2014.02.25; 2014.03.04 You may not launch the marble off the table onto the floor. a. e. b. [d1] A range of the middle 80% of distances will be found using [(mean) +/-1. will yield a range of distances that the projectile will travel when fired from the table top. . {from h = . The initial velocity of the projectile as it leaves the launcher will be estimated. The second task is to modify your system so that it is accurate enough that almost all the food bags lands in the field (and doesn’t get stuck in the surrounding trees). as shown in the “Schematic” below.28*(standard deviation)] d.a. is will also represent the middle 80% of possible final horizontal positions. This accomplishes objective (1). We chose a hitpercentage on the upper end of the desired rate in order to compensate for random error and friction. You must be able to predict roughly where the marble will land based on measurements made on the floor or on the table.Objective The objective of this lab is to respond to the following prompt (see proposal): As a member of a rescue mission your task is to launch bags of food from a cliff to a town inaccessible by road. the launcher system will be fired from the table top at a target at the location and with dimensions that correspond to the range of distance calculated in step 2. You must be able to predict where the containers will land using measurements made on the cliff itself. to the flight time found in step d. will yield the range of the middle 80% of initial velocities. [v] The ratio of the range found in step c.e. This should yield results of about 8 out of 10 hits on the target. you will not be allowed to randomly launch containers of food off the cliff. This objective to (1) launch projectiles off of a tabletop and to hit an intended target (2) at a rate of 6 to 9 times out of 10 attempts was addressed by taking the following steps: 1. Finally.b. thus accomplishing objective (2). a. [d1] The launcher will be fired 11 times at 0 degrees to the horizontal.9]. but not so accurate that all the food bags land on top of each other (crushing food). [d2] The flight time of the projectile fired from the tabletop is sqrt[(height from table)/4. [d2] The product of the initial velocity range found in step 1. 2. and the distance travelled by the projectile recorded. will be used to calculate the horizontal range of the projectile when fire from the table top onto the floor. A range of possible initial velocities will be produced to represent the middle 80% of possible initial velocities. Since this range is based on the middle 80% of possible initial velocities of the projectile.5gt^2}. However. and the time found in step 2. The bolded text summarizes the practical objective to be completed. Your second task is to (2) modify your system such that when the marble is launched on to the paper target on the floor that in 10 launches it hits the target more than 5 times but less than 10 times. The initial velocity range found in step 1. [d1] The mean and standard deviation of the distances will be calculated c.9]. Your first step is to (1) design and test a system that will launch a marble from a table. b. [v] The flight time of the projectile is sqrt[(initial height)/4. Apparatus Equiptment ● ● ● Projectile (marble) launcher and marbles Carbon paper Meter sticks (1 .2) Schematic Diagram of Marble-Launching System . (b) V ❑x = Δ d /t Where delta d is the distance travelled by the object as measured by experiment.Theory This lab requires the use of kinematic equations and the known constant g to calculate the time and distances that projectiles will travel from the origin. This expression for time is also used for the variable t in equations (a). and t is the flight time of the object given by the equation relating initial height. h: (c) t=√❑ . Given the initial horizontal velocity and initial height of an object. . h. and the time it takes to travel that distance while in freefall. whereas the horizontal value for velocity may be calculated with distances related to an initial height at ground-level. however a different value for h is used since the final value for D must represent the distance traveled when fired from the tabletop. the horizontal distance that it will travel from the origin can be calculated using the following kinematic equations: (a) D=V ❑ x t Where V sub x is the initial horizontal velocity of the object given by the equation. 2790 m 2.2254 s 5.0.1405 11 1.28*Standard Deviation Lower limit of interval of distance*` Upper limit of interval of distance*`` 1.0059 m 1.2254 s **`` V_i = 1.9) = 0.0046 m 0.1420 .148 m Initial height of projectile Projectile path time:**` Lower limit of initial horizontal velocity**`` Upper limit of initial horizontal velocity h = 0.1475 5 1.2254s = 5.148 **` t = sqrt(h/4.1485 2 1.136 *`` 1.1435 4 1.1420 + 0.0399 m/s .1415 10 1.4522 s 2.1425 9 1.1420 m 0.136 m 1.009 m T = 0.249 m t = 0.1425 8 1.0059 = 1.1365 6 1.1385 3 1.Data Tables Table 1: Distance travelled (of the marble) when fired from the ground Trial Distance (m) Trial Distance (m) 1 1.1335 7 1.0059 = 1.3031 m *Mean = (sum of Distance’s) / 11 ** Standard deviation = L❑i−L ¿2 ¿ ¿ n (1/(n−1)) ∑ ¿ 1 L n−1 σ❑ =¿ *` 1.136m / 0.0932 m/s Initial height from tabletop Projectile path time from tabletop Lower limit of interval of distance from table Upper limit of interval of distance from table H = 1.0399 m/s 5.1465 Table 2: Middle 80% of data of Distance travelled (of the marble) when fired from the ground and resulting calculations Mean Value* Standard Deviation** 1.9) = sqrt(0.249/4. Table 3: Number of projectiles that hit the target when fired from the tabletop Number of hits out of ten: 5. . 5 out of 10. .Graphs *Based on data from Table 1. **Graph shows lower and upper limits of the 80% inclusion interval calculated above (shown in black). Conclusion The first of the two objects was accomplished: a system for firing a projectile from a tabletop to hit a target based on measurements made on the ground was successfully developed. However even if it was not known. *in order to measure the 2.assumed constant in the calculations . . with target length of 0. two meter sticks were laid on the floor -end to end. The next source of error that can easily be identified is a lack of precision whilst measuring during both the ground-level trials. it may be noticed that the first data point measured during the ground-level firing trials fell considerable short of the other trial distance. The majority of the remaining projectile landed just outside of the target range (falling short of the target.as was observed.9 mm. a more intricate lab could have been conducted to account for error caused by such friction: the marble launcher could be fired at multiple firing angles . a precise target range was calculated and place 2. and may have critically skewed the data. it is reasonable to suppose that crude measuring device(s*) may have been the cause of this error. Since the error observed was on the approximately 3 mm.279 m and 2.and therefore multiple air-times whose data would reflect an inverse relationship between air-time and average initial horizontal velocity.303 m distances from the table.and a third was lined up to measure the final 20-30 cm. Additionally. Firstly.297 meters from the launcher.to decrease as the projectile moved through the air.30% more than the average-variance from the mean value.The error seen in the tabletop tests is most logically explained by air resistance which would cause the horizontal velocity of the projectile . However. This could then be used to make more accurate predictions about where the projectile would land when fired from the tabletop. or 24 mm. This however would not explain the error in the final testing because this possible outlier landed much closer to the origin than the other trials.024 meters. This possible outlier was not identified before the calculations where made. the second objective to hit the target 6 to 9 times out of ten tests was not accomplished. If the force friction caused by air resistance was known. they were not sufficiently accurate. and only 5 out of 10 projectile landed in the target range. and the tabletop-level tests.resulting in multiple arc lengths . the objective would have been met). This source of error is difficult to overcome by way of practice (it would required testing in a vacuum) however it may be accounted for in calculation. had been placed closer to the launcher by about 3 mm. 4. The final source of error is air resistance. The inaccuracy of the designed target may have been caused by any of or a combination of the following sources of error. it could be used to account for the observational discrepancy. it varied by 6 mm from the mean value . While the calculations where precise. and would have influenced the data in such a way as to move the predicted range closer to the origin rather than further .