Projectile Motion (Photogates) Name Section Theory Projectile motion is the combination of different motions in the x and y direction. In the x direction, which is taken as parallel to the surface of the earth, the projectile travels with a constant velocity x=v ox t (1) from the moment it is launched until it strikes its target. Of course, this is true only if air resistance can be ignored. In the y direction, which is taken as perpendicular to the surface of the earth, the object experiences a constant acceleration y= y o v oy t 1 2 g t 2 (2) from the moment it is launched until it strikes its target. Obviously, this acceleration is that due to gravity, g. It should be noted that when a projectile is launched at an angle θ with respect to the horizontal, the velocities in Equations 1 and 2 are the respective x and y components of the initial vector velocity v ox =v o cos v oy =v o sin (3) In solving projectile problems, obtain the flight time from the y motion and horizontal distance (range) from the x motion. Apparatus Projectile launcher, Clamp, Steel sphere, Plastic ramrod, Backstop, Lab jack, Meterstick, Paper, Carbon paper, Masking tape, Computer, Pasco 750 interface, Photogates and mounting bracket, Data Studio software. Procedure Determining the Projectile s Velocity 1. This apparatus shoots a 16mm steel sphere please exercise caution while it is being fired! If not already, turn on the computer and the 750 interface. Open the activity entitled Projectile Motion. 2. The launcher should already be set up with the photogates attached. Make sure that the sphere will be launched at the angle indicated in Data Studio (protractor on side of launcher). Place the sphere in the launcher and use the ramrod (non-capped end) to push it back until you hear 2 clicks this will be medium range. Place the wooden backdrop at the far end of the table to stop the sphere after it hits the table. 3. Click the Start button in Data Studio and fire pull straight up on the string attached to the trigger. After the sphere hits the table, click the Stop button. Data Studio will display the initial velocity of the sphere. Record this value in Table 1. 4. Repeat Step 4 until you have a total of 10 values. 5. Calculate and record the average velocity. This will be the initial velocity of the sphere for the remainder of the experiment, provided you always fire from medium range (2 clicks). Make sure this is the case. Sp07 Page 1 of 6
Velocity (m/s) 1 6 2 7 3 8 Table 1 Initial Velocity of Projectile Velocity (m/s) Average Velocity (m/s) 4 9 5 10 Firing a Projectile to the Same Level 1. Carefully remove the photogates from the launcher. They can be removed as a unit by unscrewing the mounting bracket from the bottom of the launcher. Place the assembly off to the side. 2. Carefully unscrew the launcher from its current position and attach it at the table-level position shown at left. The bolt in the channel at the back of the launcher should be at the front. Reset the launcher to the same angle as the previous procedure. Have the apparatus checked by the lab instructor before proceeding. 3. Take a test shot to see where the sphere hits the table. Tape a blank piece of paper centered at this location. Place a piece of carbon paper on top so that the impact of subsequent shots will be recorded on the blank paper. 4. Fire the sphere 10 times. Remove the carbon paper and measure the horizontal distance traveled by each shot (measure from the crosshairs on the side of the launcher). Record these distances in Table 2. Calculate and record the average distance traveled. 5. Using the average velocity in Table 1 and the launch angle, calculate the theoretical time of flight of the sphere as well as the horizontal distance it should travel. This should be done in the Calculations section of the handout. 6. Calculate and record the percent error between the average measured horizontal distance from Step 4 and the theoretical value determined in Step 5. 1 6 2 7 3 8 4 9 5 10 Table 2 Firing to the Same Level Average Distance Percent Error Sp07 Page 2 of 6
Firing a Projectile to a Different Level 1. This procedure is the same as the previous, with one exception rather than firing to the table, you will fire to a target set above the table. 2. Adjust the lab jack so that the top surface is between 15.0cm and 20.0cm off the table. 3. By trial and error, position the lab jack such that the sphere lands at roughly the center of the top surface when fired. The blank paper and carbon paper should be placed on this surface. 4. Record the data in Table 3. When measuring the horizontal distances traveled by the sphere, hold the shorter meterstick vertically at the crosshairs on the gun then measure from this over. Table 3 Firing to a Different Level Height of Target from Table 1 6 2 7 3 8 4 9 5 10 Average Distance Percent Error Sp07 Page 3 of 6
Calculations Firing a Projectile to the Same Level Time of Flight Firing a Projectile to a Different Level Time of Flight Sp07 Page 4 of 6
Pre Lab: Projectile Motion (Photogates) Name Section 1. A projectile is launched at 5.00m/s at an angle of 30º; what are the horizontal and vertical components of this velocity? 2. If the projectile in Question 1 is launched as described, how long will it be in the air until it returns to the height at which it was fired? 3. What horizontal distance will the projectile in Question 2 travel during this time? Sp07 Page 5 of 6
4. If the projectile in Question 1 is launched as described, how long will it be in the air until it reaches a height of 0.200m above the height at which it was fired? The quadratic equation here will yield 2 times one corresponds to reaching this height on the way up, and the other reaching this height on the way down. 5. What horizontal distance will the projectile in Question 4 travel during this time (the way down)? Sp07 Page 6 of 6