Lab 04 - Projectile_updated

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Dec 6, 2023

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PHYS 1: Fall 2023 Lab 04 KINEMATICS IN TWO DIMENSIONS Investigating 2D Motion: Objects under the Influence of Gravity Objective: This virtual lab activity is intended to enhance your physics understanding. It will help you make connections between predictions and conclusions, concepts and actions, equations, and practical activities. We also think that if you engage with this activity, it will be fun as well! This is an opportunity to learn a great deal. You should answer all questions as you follow the procedure in running the simulations. Click on the link below and then select the ‘ Lab ’ tab. https://phet.colorado.edu/sims/html/projectile-motion/latest/projectile-motion_en.html Use simulation controls from the bottom right controls. Click “Fire (Red Rectangle on the bottom left)” to launch the projectile or click “Erase” (next to “Fire”) to clear the projectile. You can pick different objects to shoot out of the canon by using the object selector from the top right. Fall 2023

PHYS 1: Fall 2023 You can manually adjust the settings of the projectile from the middle right projectile controls. Using projectile controls, you can set the angle, initial speed, mass, and diameter. If you wish to resemble real-world conditions, check the ‘Air resistance’ box. You can also add sound to the simulation by checking the sound box. Once you create a trajectory of a projectile, drag the blue rectangular box from the top right into the screen and place the crosshair of that rectangle along the trajectory to determine the Time, Range, and Height of the projectile at that instant. Range and height can also be verified using the “ Tape ” located on the top right. To move the tape measure, click (and hold) and drag it to the location of your choice. You can ‘ elongate ’ the tape by clicking and dragging it on the end of the tape. You can make a ‘game out of this simulation by trying to hit a target. In general, familiarize yourself with control features and displayed results. Introduction: The basic kinematics equations in one-dimensional motion are also used for two-dimensional motions. Since the two-dimensional motion is described using two components, x and y independently, the basic two-dimensional kinematics formula can be written as follows: When working with projectiles, we apply these kinematics equations with the following settings: ● An initial velocity, v 0, and initial (launch) angle θ o Horizontal component for the initial velocity is v 0 cos θ o Vertical component for the initial velocity is v 0 sin θ ● There is no acceleration in the horizontal direction: a x = 0 ● Gravitational acceleration is directed downwards: a y = -g The velocity at any point on the projectile results by applying the Pythagorean Theorem: 𝑣 = 𝑣 ? 2 + 𝑣 ? 2 The angle θ the velocity vector makes with the horizontal can be found using the following formula: = ??? −1 𝑣 ? 𝑣 ? ( ) When the kinematics equations are applied with the given specifications, the following useful equations can be derived for the case of projectiles fired from the ground . Range of the projectile: 𝑅 = 𝑣 0 2 𝑔 ?𝑖?(2θ) Fall 2023

PHYS 1: Fall 2023 Maximum height: ? ??? = 𝑣 0 2 2𝑔 ?𝑖?θ 2 Total time of flight: ? ????? = 2𝑣 0 ?𝑖? θ 𝑔 Projectile fired from a certain height: Figure 2 shows the trajectory of the projectile fired from height y 0 with an initial speed of v 0 at an angle of θ with the horizontal. The initial X- and Y- component of the velocity of the projectile is given by: ...... (3) 𝑣 0? = 𝑣 0 ???θ ....... (4) 𝑣 0? = 𝑣 0 ?𝑖?θ At any time “t”, the X- and Y- component of velocities are: ............... (5) 𝑣 ? (?) = 𝑣 0 ???θ ......... (6) 𝑣 ? ? ( ) = 𝑣 0? ?𝑖?θ − 𝑔? Where, is the acceleration due to gravity. 𝑔 = 9. 81?/? 2 If the projectile takes time “ t ” to fall to the ground, then the range (horizontal distance traveled) of the projectile is given by ..... (7) 𝑅 = 𝑣 0? × ? = 𝑣 0 ???θ×? Let us now consider just the Y - component of projectile motion. Then using kinematics equations, we can show that during this ‘free fall’, the vertical distance traveled by the projectile during time interval “t” is given by the equation, ...... (8) ? − ? 0 = 𝑣 0? ? − 1 2 𝑔? 2 At the instant when the projectile hits the ground, Equation (8) can be written as ...... (9) − 1 2 𝑔? 2 + 𝑣 0? ? + ? 0 = 0 This is equation a quadratic equation of the form: , which ?? 2 + ?? + ? = 0 we can solve to determine “ t ”. Once the time is calculated, the range, R , of the projectile can be determined using Equation (7). Fall 2023

PHYS 1: Fall 2023 Procedure for the Experiment (Simulations): Section I: Projectile fired from the ground https://phet.colorado.edu/sims/html/projectile-motion/latest/projectile-motion_en.html Part I 1. Settings: “Reset/Erase” all previous settings. Maximize the screen size. Select ‘ pumpkin ’ from the top right. Set the projectile angle to 55 degrees and the initial speed to 18 m/ s. Keep the ‘launch-height’ at 0.0 m, mass and diameter remain in the default setting. Also ‘turn-off’ the air resistance. 2. “Launch” the pumpkin. 3. Drag the tape measure located on the top center of the screen to measure the ‘maximum-height’ and the range of the projectile. Record your measurements. Maximum height (y max ) = 11.08 m Range (x) = 30.50 m [3 + 3 = 6 Points] 4. Calculate the ‘ maximum height ’ and the range using the angle and initial speeds set at step 1 using formulas provided in the ‘Introduction’ section. You must show your work to get credit. [4 + 4 = 8 points] Calculated Maximum height (y max ) = 11.08 m ● = = 11.08 ? ??? = 𝑣 0 2 2𝑔 ?𝑖?θ 2 ? ??? = 18 2 2 (9.81) ?𝑖?(55) 2 Calculated Range (x) = 31.04 m ● = 𝑅 = 𝑣 0 2 𝑔 ?𝑖?(2θ) 𝑅 = 18 2 9.81 ?𝑖?(2(55)) = 31. 04 5. Is there a difference between your measurement and your calculated result? Compare the calculated results with the measurements. Explain with the reasoning if there are differences. [2 Points] ● There is a difference between what I calculated and my actual measurements. I believe that the differences are because the calculated results are based on idealized physics equations, assuming no air resistance and perfect conditions. In contrast, the measured simulation results are influenced by the accuracy and settings of the simulation itself. Small discrepancies between the idealized calculations and real-world simulations can occur due to factors such as simulation accuracy and the handling of physics within the software. Rounding in the calculations and measurements can lead to minor differences between the values. Fall 2023

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