Projectile Motion and Kinematics

Projectile Motion and Kinematics Carlos Zabaleta February 10, 2024 Prof. Irina Golub

Purpose The objective of this laboratory experiment was to explore the correlation between frictional and normal forces, as well as to determine the magnitude of the frictional force. The investigation involved utilizing the phET simulation and placing objects of varying masses on a board, then exerting force until they initiated motion.

Introduction In this activity, we're dealing with basic principles like gravity, how fast things fall, the different parts of a force, how fast an object starts moving, how heavy it is, the angle it's launched at, how far it goes, how high it goes, air slowing it down, and how these factors connect. Projectile motion means how something moves through the air when you shoot it. In the lab, we'll use a simulator to see how things like weight, size, and what you shoot affect the way they move. I'll use simple equations to figure out how long it takes, how far it goes sideways, and how high it goes. We're assuming that gravity pulls things down with a speed of -9.80m/s^2.

Procedure In the first part, I'll check out how the starting speed affects how far, how high, and how long something travels through the air. I'll keep the angle and object the same, but I'll shoot it at different speeds and measure the time, distance, and height for each try, doing this 10 times. Then, I'll repeat the same process with a different thing I'm shooting, making the same number of measurements with the same speeds as before. In the second part, I'm going to look at how things speed up when there's no air slowing them down compared to when there is air resistance. I'll start with the same speed, size, angle, and weight for the objects I'm shooting. I'll see how the acceleration changes when I adjust the angle of the cannon. After that, I'll look at the velocity (how fast things are going) with the same criteria as before, tracking the parts going sideways and up and down during the motion. Then, I'll use the same setup to see how mass, the thing I'm shooting, gravity, size, height, air slowing it down, and some drag thing affect the motion. I'll use different values and do this a bunch of times to see how height, distance, and time are affected by mass, object, gravity, size, height, and air resistance.

2 m/s 1.28s 2.55m 0m 4 m/s 1.28s 5.11m 0m 6m/s 1.28s 7.66m 0m 8m/s 1.28s 10.22m 0m 10m/s 1.28s 12.77M 0m 12m/s 1.28s 15.33m 0m 14m/s 1.28s 17.88m 0m 16m/s 1.28s 20.43m 0m 18m/s 1.28s 22.99m 0m 20m/s 1.28s 25.54m 0m 1. What do these values tell you? From the numbers, I can say that the time and height stay the same no matter how fast we start things. In all our tries, the object fly for 1.28 seconds to and ended up at a height of 0 meters. But, as we made the object go faster at the start, it went farther . Nevertheless, the distance covered expanded progressively with higher initial speeds, indicating a positive correlation between the initial speed and the range of the object. 2. Change to a different projectile like a car and repeat the same steps (1-8). What the results do tell you? Projectile selected: piano Initial Speed Time Range Height 2 m/s 1.28s 2.55m 0m 4 m/s 1.28s 5.11m 0m 6m/s 1.28s 7.66m 0m 8m/s 1.28s 10.22m 0m 10m/s 1.28s 12.77M 0m 12m/s 1.28s 15.33m 0m

14m/s 1.28s 17.88m 0m 16m/s 1.28s 20.43m 0m 18m/s 1.28s 22.99m 0m 20m/s 1.28s 25.54m 0m Even when the projectile object was changed from pumpkin to piano, the results for time, range, and height remained the same for all ten trials. This tells me that the weight or mass of an object does not affect its projectile motion. Obviously, a piano has more mass and weight than a pumpkin does. However, the projectile motion of both objects had the same time, range, and height for each corresponding initial speed trial. Part II: Vectors Initial setup and investigating gravitational acceleration. 1. Uncheck the “air resistance box”. Set the following: diameter = 0.8 m, mass 5 kg, initial speed = 12 m/s and the cannon angle = 45º. Click the “slow” button at the bottom to watch the simulation more carefully. 2. Click the box that says “acceleration vectors” 3. Fire the cannon. You will see the cannonball leave the cannon, with an acceleration vector. 4. Notice and record your answer for the questions: What is the direction of the vector? and What does this vector represent? The direction of the vector is pointing downwards. The vector represents the acceleration of the cannonball with a 5kg mass, 45º angle, and initial speed of 12m/s. 5. What do you observe about the length of the vector throughout its flight? The length of the vector remains the same throughout the duration of the cannonball's flight.

12. Summary: What have you discovered about the acceleration due to gravity of an object in flight with regards to the angle of launch? There is no change in the acceleration due to gravity of an object in flight. The angle it was launched from does not affect the acceleration vector that gravity will impose on the object. Initial setup and investigating velocity. 1. Click the yellow erase button and unclick the acceleration vectors box. Click the “velocity vectors” box. Click on “components” just above it. This will track velocity in both the x and y directions. 2. Start with the same settings as for the gravitational acceleration investigation in the previous part. 3. What do you notice about the velocity vector in the y direction? Describe what happens to its length and direction throughout the flight? Be specific.

The velocity vector in the y direction changes regarding the parabolic motion of the object. It begins pointed upward until the maxima of the parabola is reached and then the vector begins growing downwards. The length of the vector is proportional to the object's motion. 4. At what point does it seem like there is no velocity vector in the y direction? At the highest point of the cannonball's path, or the Y maximum. 5. Describe in your own words what is happening to the velocity in the y direction as the cannonball leaves the cannon and flies through the air. The velocity in the y direction begins at its highest point when the cannon is fired and steadily decreases pointed upwards when the cannon is first fired. When the cannonball reaches the midpoint in its parabola, or the maximum, the y direction vector disappears for a moment and then begins to grow downwards. 6. What do you notice about the velocity in the x direction? The velocity in x direction in a projectile motion remains constant in magnitude and direction. 7. Change the angle of the cannon to 65º, and repeat steps 1-6. 7.1 The velocity vector in the y direction decreases in length throughout the flight. Its direction is the same as the before mentioned velocity vector in that it begins pointed. 7.2 When the cannonball reaches its highest point, the Y maximum. 7.3 The velocity in the y direction begins at its highest point when the cannon is fired and steadily decreases pointed upwards when the cannon is first fired. When the cannonball reaches the midpoint in its parabola, or the maximum, the y direction vector disappears for a moment and then begins to grow downwards.

Part II: Acceleration due to gravity determination: 1. Choose the Lab option in your simulator. 2. Uncheck the “air resistance box”. 3. Set the following: initial speed = 16 m/s and the cannon angle = 54º. 4. Use the crosshair tool and measure the maximum height, the range, and the time in flight. 5. Use the kinematics equations to calculate with these given the acceleration due to gravity. 6. Compare your calculated value to the accepted value for g = 9.80 m/s 2 (Calculate your percent error). The crosshair tool measured a maximum height of 8.55m at 1.32 seconds, a total flight time of 2.64s, and a range of 24.84m.

Conclusion In part one of the experiment, I observed that adjusting the initial speed doesn't change the time and height of the projectile motion. All the trials had a flight time of 1.28 seconds and reached a final height of 0 meters. However, the range increased as the initial speed went up, showing a

Finally, when I calculated height, total time, and range using kinematic functions, my results were close to those from the simulator where gravity is -9.80m/s^2. The percentage errors were minimal at 0.11% for height, 0.075% for time, and 0.17% for range, mainly due to using a slightly different gravity value. Overall, I argue that the simulator provided more accurate results than my kinematic equations.