PHY 101L Module Three Lab Report Projectile Motion (1)

PHY 101L Module Three Lab Report Projectile Motion Name: Thomas Hubert Date: 08/28/2023 Complete this lab report by replacing the bracketed text with the relevant information. Activity 1: Horizontal Projectile Motion Data Table Activity 1 Table 1 Trial Sphere θ a = 0.71(9.8)sinθ 𝒗 𝒙 = √(2 𝒂𝒔 ) 𝑡 = √(2 ℎ / 𝒈 ) Calculated Distance 𝑥 = 𝒗 𝒙 𝑡 Actual Distance Percent Difference 1 Steel 45 4.8508 2.9219 3.8598 0.1128 0.33 70.74 2 Steel +5° 5.3301 3.0628 3.8598 0.1182 0.35 66.23 3 Steel +10° 5.6997 3.1672 3.8598 0.1222 0.38 67.84 4 Acrylic 45 4.8508 2.9219 3.8598 0.1128 0.30 62.40 5 Acrylic +5° 5.3301 3.0628 3.8598 0.1182 0.31 61.87 6 Acrylic +10° 5.6997 3.1672 3.8598 0.1222 0.33 62.97 I noticed my equations only had a 5 percent error when I used the equation a= (0.71)sinθ Activity 1: Questions 1. Did the sphere in the experiment always land exactly where predicted? If not, why was there a difference between the distance calculated and the distance measured? The sphere in the experiment did not always land exactly where predicted. This could be because of things like air resistance or friction. There can also be human error when measuring distances and recording times. 2. Why is it important to use the grooved ruler to ensure that the sphere leaves the table in a horizontal direction? It is important to use the grooved ruler to ensure that the sphere leaves the table with a horizontal velocity. If the sphere is not released in a horizontal direction, it will curve as it falls and won’t travel as far. 3. If the same experiment were performed on the moon, what would be different? If the same experiment were performed on the moon the sphere would not curve as much when it falls because there is less gravity on the moon. The sphere would also travel farther because there is less air resistance. 4. What is different about the vertical component of the sphere’s velocity and the horizontal component of the sphere’s velocity once the sphere leaves the table? The vertical component of the sphere's velocity increases due to the force of gravity, while the

horizontal component of the sphere's velocity remains constant unless there is a force acting on it. 5. If the same experiment were repeated with the same angles, but from a taller table, how would the results change? If the same experiment were repeated with the same angles but from a taller table the sphere would travel further because it has more time to fall. The vertical velocity of the sphere would also increase. Activity 2: Exploring Projectile Motion with a Simulation In this activity, you will explore how altering the variables of the initial launch condition of a projectile affects the projectile’s trajectory. Adobe Flash is required for the PhET projectile motion simulator website. The simulation will allow you to change the following variables: Angle : This is the angle between the launch vector and the horizontal. Initial Speed: This is the speed of the projectile when it leaves the barrel of the cannon. Mass: This is the mass of the projectile. This is only a factor if air resistance is selected. Diameter : This is the diameter of the projectile. This is only a factor if air resistance is selected. Initial Position : You can control the initial position ( x and y ) by dragging the cannon with the mouse. You can measure the height by using the tape measure icon. Air Resistance : There is a check box for air resistance. For this activity, make sure the box is not checked. Air resistance will be ignored for this activity. Changing the initial conditions will affect the following variables, which are indicated in windows at the top of the simulation’s screen: Range : This is the horizontal distance measured from the launch position to where the projectile lands on the ground, or at the point where y = 0. The y coordinate for the projectile’s landing point is fixed in the simulation, but the target icon can be moved to any position on the screen. Height : This is the vertical displacement from the launch position. The simulation briefly displays the height of the projectile at 1-second intervals. To find the maximum height, use the tape measure icon. Time : This is the total time of flight of the projectile from time of launch to time of impact; black crosses indicate the location of projectile along the trajectory at 1-second intervals. Fire : This button launches the projectile. Erase : This button clears the trajectory paths off the screen. Zoom : There are two magnifying glass icons that allow you to zoom in and out. 1. Open/Access the projectile motion PhET simulation module located at: https://phet.colorado.edu/en/simulation/projectile-motion 2. Take some time to locate and become familiar with the controls. 3. Set the initial conditions to those listed in Table 2. 4. Complete Table 2 by changing the height of the launch and recording the data for range, maximum height, and time. Note: The angle, initial speed, mass, and diameter of the projectile can be entered using the

Ball 2 1 7.3 0.25 20 10 Bowling Ball 18.27 1.61 0.93 3 1 7.3 0.25 20 20 Bowling Ball 28.72 3.38 1.53 4 1 7.3 0.25 20 30 Bowling Ball 36.97 6.1 2.13 5 1 7.3 0.25 20 45 Bowling Ball 41.75 11.19 2.95 5 1 7.3 0.25 20 50 Bowling Ball 40.98 12.96 3.19 7 1 7.3 0.25 20 60 Bowling Ball 35.88 16.29 3.59 8 1 7.3 0.25 20 70 Bowling Ball 26.57 19.00 3.88 9 1 7.3 0.25 20 80 Bowling Ball 14.12 20.77 4.07 10 1 7.3 0.25 20 90 Bowling Ball 0.00 21.39 4.13 Activity 2: PhET Simulation Data Table 4 Table 4 Variable: Initial Speed Trial Initial Height (m) Mass (kg) Diameter (m) Initial Speed (m/s) Angle (°) Projectile Range (m) Height (m) Time (s) 1 1 7.3 0.25 5 0 Bowling Ball 2.26 1.00 0.45 2 1 7.3 0.25 10 0 Bowling Ball 4.52 1.00 0.45 3 1 7.3 0.25 15 0 Bowling Ball 6.77 1.00 0.45 4 1 7.3 0.25 20 0 Bowling Ball 9.03 1.00 0.45 5 1 7.3 0.25 25 0 Bowling Ball 11.29 1.00 0.45 6 1 7.3 0.25 30 0 Bowling Ball 13.55 1.00 0.45 Activity 2: Questions 1. For Table 2, the initial speed and launch angle were kept constant, and the height was increased. Your data should show that the horizontal range of the projectile increased with each trial. If the initial speed and launch angle were constant, how did increasing the height change the horizontal range? Increasing the height allowed the “bowling ball” to travel horizontally for a longer time before

hitting the ground, increasing the distance(range). 2. For Table 3, the height and initial speed were kept constant, and the angle was increased. How did the launch affect the range? How did the launch angle affect the time of flight? Increasing the launch angle increased the range until the range peaked at 45 ° and the range began to decline with any further increase in the launch angle. The time of flight increased steadily as I increased the launch angle. The steeper the angle, the more time the projectile spends in the air. 3. Examine the data in Table 3. You should see that several angles have the same or nearly the same horizontal range. What do you notice about these pairs of angles? What is different about the trajectories of the projectiles when fired from these angles? Based on the data in Table 3, I notice that launch angles above and below 45 degrees have very similar ranges. The ranges at 30 degrees and 60 degrees are close (36.97 m vs. 35.88 m). At 30 degrees the projectile has a flatter trajectory, so more of its initial velocity is directed horizontally resulting in more horizontal distance traveled. At 60 degrees the trajectory is steeper, so more of the initial velocity is directed vertically. This results in less horizontal distance, but the projectile also spends more time in the air on the steeper trajectory which allows it to travel farther. The main difference between these paired angles is the shape of the trajectory. At 30 degrees, the path is lower and flatter. At 60 degrees, the path is higher and steeper. But the net horizontal distance covered can be similar due to the tradeoff between horizontal velocity and time of flight. 4. For Table 4, the launch angle and height were kept constant, and the initial speed was increased. You should have noticed that the time of flight was constant as well. What does that say about two- dimensional motion? The time of flight being consistent says that horizontal and vertical motion are independent. This is because the time of flight only depends on the initial height and the launch angle. The initial speed only affects the horizontal range of the projectile. 5. How could the speed of the projectile be determined from test-firing the cannon? The speed of the projectile could be determined from test-firing the cannon by measuring the horizontal range and the time of flight. Speed = Distance/Time