QUESTION 3: Discuss any differences between the observed and predicted values in Table 1. QUESTION 4: Which angle produces the maximum range? Is this what you expect from what you have learned? QUESTION 5: Do any two launch angles produce the same range? Which ones? What must be true for the cannon to reach the same range for two different launch angles? Investigating air resistance Reset the simulation. Set the launch angle to 45 degrees. Set the mass of the projectile to its lowest value. Fire the cannon and record the range. Set the mass of the projectile to its highest value. Fire the cannon and record the range. QUESTION 6: How do the two ranges compare? Explain in your own words why this is so. Reset the simulation Set the launch angle to 25 degrees. Set the diameter of the projectile to 1 meter. Make sure the box for Air Resistance is not checked. Fire the projectile and record the range in Table 2. Check the box for Air Resistance. Fire the cannon. Record the range in Table 2. Calculate the difference between the two ranges. Repeat the above procedure for 45 degrees and 65 degrees. QUESTION 7: Is there a clear trend in the difference caused by air resistance? Explain. QUESTION 8: Before, 25 degrees and 65 degrees produced the same range with no air resistance. Do they have the same range with air resistance? Why are the two different? highest point is marked by a yellow dot. Use the sensor to measure the maximum height of a trajectory by placing the crosshairs on the yellow dot. Press the circled arrow in the lower right to reset the simulator. Angle the cannon to 45 degrees and fire the cannonball. Now check the box for "Air Resistance", and slide the "Diameter" of the projectile to its maximum value. Fire the cannon and observe the difference. Procedure One- versus Two-dimensional motion Reset the simulation. Raise the cannon platform to 10m. Set the initial velocity of the cannon shell to zero. Set the angle of the cannon barrel to zero degrees. Fire the cannon. Using the sensor, inspect the landing point and record the time that it took the projectile to fall. Set the initial velocity to 10 m/s and fire the cannon. Using the sensor, inspect the landing point and record the time that it took the projectile to fall. QUESTION 1: How long did it take the ball with zero velocity to fall compared with the time it took the ball with an initial velocity to fall? QUESTION 2: In your own words, explain why the time of flight of the two trials compare the way they do. Predicting two-dimensional motion If an object is launched with an initial velocity vo at an angle of 0 with a gravitational acceleration of g, then theory predicts that the range of the projectile R can be predicted by the following equation: v sin20 R = g Table 1 lists several values of 0. Since this class does not use trigonometry, the table also includes the value of sin2 0 for your convenience. Using the equation, fill in the predicted range in Table 1 for all values of 0, given an initial velocity of 15 m/s and a gravitational acceleration of g=9.81 m/s. Observing two-dimensional motion Reset the simulation Set the initial velocity to 15 m/s. Set the launch angle to 25 degrees. Fire the cannon. Measure and record the range of the projectile in Table 1. Calculate the difference between the observed and the predicted values of the range. Repeat the above procedure for all values of 0 in Table 1. QUESTION 3: Discuss any differences between the observed and predicted values in Table 1. QUESTION 4: Which angle produces the maximum range? Is this what you expect from what you have learned? Projectile motion involves the two-dimensional motion of an object which travels vertically under the influence of gravity while moving horizontally with some initial speed. Some of the details of projectile motion are outside of the scope of our course since they involve trigonometry, but we can still use computer tools to take care of these details so that we can concentrate on the results. A freely-falling object moving in two dimensions will have two parts to its velocity; a vertical component controlled by gravity, and a horizontal component set by its initial velocity. For a perfect freely-falling object, the vertical velocity and position are exactly what is predicted by the equations of motion with an acceleration of g in the previous chapter. The horizontal velocity and position are what is expected for an object with zero acceleration. In free fall the two are independent; the vertical motion does not affect the horizontal motion. The situation changes when we look at the more realistic case of an object experiencing air drag. In this case, both the vertical and horizontal motion experience an extra acceleration due to the drag force, changing the trajectory of the object. In this laboratory, you will use a computer simulation to investigate the properties of projectile motion. Preparation Open or print the laboratory report document. Make all of your recordings on the document. You may find it convenient to record your handwritten results on a printed page, but you must type them into a document to submit at the end of the assignment. Run the projectile motion simulator at https://phet.colorado.edu/sims/html/projectile-motion/latest/projectile-motion en.html Take a moment to play with the simulator and learn how the controls work. Press the red button on the bottom bar to fire the cannon. Observe the trajectory on the screen. Click and drag the cannon barrel to change the angle. Fire the cannon and observe the new trajectory. Carefully position the mouse over the cross on the cannon where it pivots. Click and drag up to raise the cannon platform. Fire the cannon and observe the difference. You can measure the range of a projectile in two ways; with the tape measure or with the target circle. I find the target circle easiest. Click and drag the target circle so it is centered on a landing point and observe the range. If you like, practice with the measuring tape. Choose which method suits you best. In the white box at the top are two measuring devices, a sensor and a tape measure. Drag the sensor out of the box and move it so that the crosshairs are on the landing point of a projectile. Observe the information given about the landing point. Observe that in each trajectory, the Data Tables Table 1 Sin(20) Predicted R Observed R Difference 25 0.766 35 0.940 45 1.000 55 0.940 65 0.766 75 0.500 Table 2 Range with no drag Range with drag Difference 25 45 65