(doneeeeee)FIRSTLAST1_FIRSTLAST2_PHYS182A_195L-LAB4_WITHDATAMUNEEEERRRRRR

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Apr 3, 2024

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PHYSICS 182A/195L LAB REPORT - LAB 4: PROJECTILE MOTION Lab 4: Projectile Motion San Diego State University Department of Physics Physics 182A/195L TA: Lab partner 1: Neimiah Aitegeb Lab partner 2: Muneer Yassin Date: Score: Data has been entered in blue. Theory During projectile motion, there is only one force: the force due to gravity: . By integrating the above equation, we obtain the velocity vector as a function of time: where and are the x and y components of the initial velocity. Integrating again, we obtain the position vector: where and are the initial x and y coordinates of the projectile. In other words, , and . To simplify our equations, throughout this lab we will assume that , so , and . Range The first quantity we will be interested in calculating is the range of a projectile. This is equivalent to the maximum value of the x-component of , which is when is maximum. So how do we know when is maximum? After some thought, you should conclude that the maximum value of occurs when is equal to zero, i.e., when the projectile hits the ground. We can solve for by setting :
1 Department of Physics We solve by factoring: , And so finally, is . To find the range we simply plug in into : . Suppose that we know the initial speed and angle that the object will be launching from. (These are things we can measure.) We can write the components of the initial velocity vector as . Thus, the range can also be written as: Altitude calculation Instead of launching a projectile from and , imagine launching it from some nonzero altitude . To keep things simple, let's also assume that the object is launched with an initial vertical speed . Under these conditions, our general equation for : simplifies to: As you can see, the initial altitude h of the projectile depends only on and . Therefore, if we know the time of flight (the time when reaches 0) that a projectile is in motion, then we can solve for it’s initial altitude:
PHYSICS 182A/195L LAB REPORT - LAB 4: PROJECTILE MOTION Procedure Part I: Range 1. To make your results more consistent when launching the ball, always pull on the black cord (see Figure 1) with a quick short pulse. Do NOT pull slowly. Always make sure that everyone is clear before firing! 2. The angle should be set at 20°. Place the ball in the launcher and depress the plunger one "click" to the short range setting. 3. Launch the ball and note the landing location. Place a blank sheet of paper at this location and tape it in position as shown in Figure 2. Cover with a sheet of carbon paper. You do NOT need to tape the carbon paper. 4. Launch the ball again, and confirm that the contact point is marked. Launch the ball a total of 5 times. 5. Use a Meter Stick (see Fig. 3) to measure the ranges. This distance should be measured from the center of the launch position of the ball as shown in Figure 4. Measure each landing point separately (see Fig. 5), and then calculate the average range. If you mess up or the ball lands dramatically far away from the other points, just take another trial and omit the odd point. 6. Enter the average range for 20° in Table 1 in the Data section. 7. Repeat the procedure to fill out the rest of the first column of Table 1. Part II: Altitude In this section, the ball is launched horizontally from a height above the table, as shown in Figure 6. 1. Fasten the launcher horizontally (see Fig. 6). Take the screws from Position 1 and move into Position 2. When the launcher is completely horizontal, the angle should read 00. 2. Use the Table Clamp and Metal Rod to support the launcher. Set the launcher 0.10 to 0.20 m above the table. Record the exact height in Table 3. 3. Slide the launcher forward so that it projects out past the edge of the bracket. This makes it easier to use with the Photogates attached.
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4. Make sure the launch angle is exactly zero and then securely fasten all the screws. 5. Plug the Time of Flight pad into Digital Input #4, and position it at the landing position of the ball. 6. Attach the Photogates to the launcher, as shown in Figure 6. You want the position of the photogates to be as close to the launcher as possible. Plug the first Photogate into Digital Input #1 and the second Photogate into Digital Input #2. 7. Depress the plunger for long range, then click on Record. Launch the ball. The speed and time of flight is displayed to the right. 3 Department of Physics 8. Click on Stop, and record the values in Table 2. Repeat for two more runs on the long range setting. 9. Repeat for the launcher set for medium range and for short range. Record three good trials for each launcher position. Figure 1: Launching Ball Trigger Figure 2: Range Landing Area Figure 3: Measuring the Range Figure 4: Launching from Center
Figure 5: Landing Point Separation Figure 6: Horizontal Launcher Setup Data Table 1: Range as a function of initial angle. PHYSICS 182A/195L LAB REPORT - LAB 4: PROJECTILE MOTION Angle (degrees) Measured Range (m) Theoretical Range (m) Percent error (%) 20 .801 .831 3.61 30 1.13 1.12 .893 40 1.28 1.27 .787 45 1.29 1.29 0 50 1.25 1.27 1.57 60 1.12 1.12 0 70 .835 .831 .481 Table 2: Speed and time of flight Range setting Measured speed (m/s) Measured time of flight (s) Short (1) 3.58 0.20
Short (1) 3.53 0.21 Short (1) 3.57 0.18 Medium (2) 4.68 0.20 Medium (2) 4.66 0.21 Medium (2) 4.67 0.17 Long (3) 6.09 0.19 Long (3) 6.1 0.20 Long (3) 6.13 0.22 Table 3: Exact height of launcher h (m) 0.18 5 Department of Physics Analysis 1. Once you complete Table 2, you will have determined the initial speed of the ball for the short range setting of the launcher, . Use this information to go back and fill out the rest of Table 1. Compute the percent error of your measurements from Part I. 2. Copy your PASCO Range as a function of the initial angle graph for part I into the box below. Right click on the edge of the PASCO graph object and select “Copy Display”. Paste into this document with “Ctrl+v”. Graph 1: Range as a function of initial angle
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Questions 1. What value of the initial angle maximizes the range? PHYSICS 182A/195L LAB REPORT - LAB 4: PROJECTILE MOTION 45 Degrees will give you the farthest range. 2. Is the time of flight for short range less, more or about the same as the time of flight for medium and long range? It is about the same for all three ranges, this is because gravity is constant and because the ball is being launched from the same height each time the flight time will remain unchanged. 3. Calculate the average time of flight for all runs combined. .198s
4. Using this average time, calculate the height, h, the ball drops ( ): .192 m 5. Compare to the value for "h" that you measured on the previous page, using the % error calculation. 6.25% 7 Department of Physics

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