Fall2023 Projectile Motion Lab Online-1

Projectile Motion Lab Online Purpose The purpose of this activity is to examine some of the basic behaviors and properties of simple projectile motion. Among those properties and behaviors that will be examined are, how does the initial angle at launch affect the range of the projectile? Theory Projectile motion is a form of motion in which an object (called the projectile) is launched at an initial angle θ , with an initial velocity . While the projectile is in flight, only the force of gravity (we are ignoring any air resistance) is acting on the projectile. Since, near the Earth’s surface, the force of gravity causes masses to be accelerated downwards at a constant rate of we can use the simple Kinematic equations to describe projectile motion. Using the standard coordinate system where the x-direction is purely horizontal and the y-direction is purely vertical, we obtain the following equations of projectile motion for the y-direction: Since gravity acts purely in the vertical direction, and we have no other forces acting on the projectile during flight, the acceleration in the x-direction is zero: This results in our kinematic equations in the x-direction reducing to the following; Assuming that the initial angle θ is measured from the horizontal, then the projectile’s velocity components are given by; From the above diagram we can see the behaviors of the velocity vector, and its components, of a projectile while it is in flight. The x-component is constant through the entire flight while the y- component is constantly changing. The y-component is equal to zero when the projectile is at its maximum height, and therefore the velocity vector is at its minimum value when the projectile is at its maximum height. The x-displacement, the projectile goes through during its flight is called ‘the range’ of the projectile. One of the things we will look at in this activity is how changing the initial launch angles affects the range of the projectile. Set Up • Go the following website https://phet.colorado.edu/en/simulation/projectile-motion • Now you should see the following screen.

• Click on ‘DOWNLOAD’ to download the simulator program, and then open the software once it has downloaded. • Once it opens you should see the following. • Click the option furthest to the right called ‘Lab” • Now you should see the following. • On the right set the mass to 1.00 kg, the diameter to 0.10 m, make sure gravity is set to 9.81 m/s 2 , and finally make sure Air Resistance is NOT checked. • In the white box at the bottom left of the screen set the initial speed to 15 m/s. • In the white box at the top of the screen and off center to the right you will find a ‘device’ you can drag around the screen to measure the Time of Flight, Range, and Height. We will be using this mostly to measure the range during the lab, and occasionally the time of flight. Procedure for part 1 • Make sure the height of the cannon is set to 0 m. You can read the current height of the cannon directly to its left. If it is not set to 0 m, ‘click and hold down’ on the cannon to set the height to 0 m. • Set the ‘cannon’ to an angle of 25 0 . • Click on the red button near the bottom left of the screen to ‘fire’ the cannon. • Use the ‘device’ to measure the range of the projectile, and record the range in table 1. • Repeat this process for all the angles listed in table 1. • For 45 0 also measure and record the time of flight. Procedure for part 2 • Now ‘click and hold down’ on the cannon to raise the height of the cannon to 10 m. • Set the initial velocity of 12 m/s. • Set the launch angle to 0 0 . • Click on the red button near the bottom left of the screen to ‘fire’ the cannon. • Use the ‘device’ to measure the Range of the projectile, and record the range in table 2. • Repeat process for all the angles listed in table 2. • For 45 0 also measure and record the time of flight. Analysis of Projectile Motion Lab Online

• Using equation calculate the theoretical range for your projectile with the initial launch angle of 45 o . (5 points) Vix = Vcos(theta) = 15cos(45) = 10.61 Δ x = Vixt = 10.61 Δ x = 22.92 • Calculate the % error between your measured range, and your theoretical range for the initial launch angle of 45 o . (5 points) Percent error = 22.92 - 22.94/22.92 x 100 = 0.087% • Do the results of our experiment confirm theoretical predictions? Defend your answer. (10 points) Yes I think the results do confirm theoretical predictions because the percent error is low. This means that the expected value is near the theoretical value

Table 2: Uneven surface (20 points) Initial Height: 0 0 5 0 10 0 15 0 20 0 25 0 30 0 35 0 40 0 17.1 18.3 19.5 20.6 21.5 22.1 22.5 22.5 22.2 45 0 50 0 55 0 60 0 65 0 70 0 75 0 80 0 85 0 21.5 20.4 18.9 17.0 14.7 12.2 9.4 6.4 3.2 Time of flight for 45 0 :___2.53____ • Using Excel or some other graphing software, Graph Range vs. Initial Launch Angle. Is the graph symmetric? If so, where is the axis of symmetry? Turn this graph in with your lab worksheet. (10 points) This graph is asymmetrical meaning there is no axis of symmetry • Using the equation calculate the time of flight for the initial launch angle of 45 o . (5 points) Vy = Vsin(theta) = 12sin(45) = 8.49 Y = Yi + Viyt - 1 / 2(9.81)t^2 t = 2.54 • Using equation calculate the theoretical range for your projectile with the initial launch angle of 45 o . (5 points) Vix = Vcos(theta) = 12cos(45) = 8.49