Nae: Date: Partner(s): Period: Projectile Motion Lab (2019) Object: Measure the velocity of a ball using two Photogates and coputer software for tiing. Apply concepts fro two-diensional kineatics to predict the ipact point of a ball in projectile otion. Take into account trial-to-trial variations in the velocity easureent when calculating the ipact point. Introduction: You have probably watched a ball roll off a table and strike the floor. What deterines where it will land? Could you predict where it will land? In this experient, you will roll a ball down a rap and deterine the ball s velocity with a pair of Photogates. You will use this inforation and your knowledge of physics to predict where the ball will land when it hits the floor. Materials: Figure 1 coputer Vernier coputer interface Logger Pro two Vernier Photogates ball (1 to 5 c diaeter) asking tape plub bob rap two ring stands two right-angle claps eter stick or etric easuring tape carbon paper
Procedure: 1. Set up a low rap ade on a table so that a ball can roll down the rap, across a short section of table, and off the table edge as shown in Figure 1. 2. Position the Photogates so the ball rolls through each of the Photogates while rolling on the horizontal table surface (but not on the rap). Approxiately center the detection line of each Photogate on the iddle of the ball. Connect Photogate 1 to DIG/SONIC 1 of the interface and Photogate 2 to the corresponding second port. To prevent accidental oveent of the Photogates, use tape to secure the Photogates to the table. 3. Mark a starting position on the rap so that you can repeatedly roll the ball fro the sae place. Roll the ball down the rap through each Photogate and off the table. Catch the ball as soon as it leaves the table. Note: Do not let the ball hit the floor during these trials or during the following velocity easureents. Make sure that the ball does not strike the sides of the Photogates. Reposition the Photogates if necessary. 4. Open the file 08A Projectile Motion in the Physics with Vernier folder. A data table and two graphs are displayed; one graph will show the tie required for the ball to pass through the Photogates for each trial and the other will display the velocity of the object for each trial. 5. You ust enter the distance, Δd, between Photogates in order for Logger Pro to calculate the velocity. The progra will divide this distance by the tie interval Δt it easures to get the velocity (v = Δd/Δt). Carefully easure the distance fro the bea of Photogate 1 to the bea of Photogate 2. (It ay be easier to easure fro the leading edge of Photogate 1 to the leading edge of Photogate 2.) To successfully predict the ipact point, you ust enter an accurate easureent. Adjust the gate separation using the control on the Logger Pro screen. 8 to 10 c photogate 1 photogate 2 Figure 2
Procedure: (cont.) 6. Click. Check to see that the Photogates are responding properly by oving your finger through Photogate 1 and then Photogate 2. Logger Pro will plot a tie interval (Δt) value for each instance you run your finger through Photogate 1 or Photogate 2. Click, then click again, to clear the trial data and prepare for data collection. 7. Roll the ball fro the ark on the rap, through both Photogates, and catch the ball iediately after it leaves the table. Repeat nine ties. Take care not to bup any of the Photogates, or your velocity data will not be precise. Data collection will stop after two inutes. If you need ore tie, click to restart, choosing Append. After the last trial, click to end data collection. Record the velocity for each trial nuber in the first data table. 8. Inspect your velocity data. Did you get the sae value every tie? Deterine the average, axiu, and iniu values by clicking once on the velocity vs. tie graph and then clicking the Statistics button,. What one value would be ost representative of all ten easureents? 9. Carefully easure the distance fro the table top to the floor and record it as the table height in the data table. 10. Using the table height you just easured, go to the calculations page and calculate the tie the ball will be in the air. After you coplete the calculation return to step 11. 11. Tape two pieces of blank white paper together (top to botto, not side to side). Tape the two pieces of paper to the floor, aking sure the plub bob is over the edge of the paper. 12. Using the plub bob as a guide, ark the paper directly under the plub bob on the paper; it will serve as your floor origin. plub bob floor origin Figure 3
Procedure: (cont.) Data: 13. In the calculations section, use your axiu, iniu, and average velocity values to calculate the axiu, iniu, and average distances fro the floor origin to the ipact point where the ball will hit the floor. (Using the axiu and iniu velocities, as well as the average velocity will allow us to account for the variations you saw in the Photogate velocity easureents.) 14. Mark your predicted axiu, iniu, and average ipact points on the white paper. 15. Place the carbon paper on top of the white paper. Make sure you have the correct side of the carbon paper facing down. 16. After your instructor gives you perission, release the ball fro the arked starting point, and let the ball roll off the table and onto the carbon paper. Repeat the process for a total of five runs. 17. Take off the carbon paper to reveal the arks where your ball landed. 18. Using a copass, ake a circle that just encopasses all of the data points. Using the center of this circle, easure the distance to the ark you ade on the white paper under the plub bob. This will be your actual ipact distance. 1. Measure the velocity of the projectile for each trial. (Do not let the ball hit the ground) Trial No. Velocity (/s) 1 2 3 4 5 6 7 8 9 10
Data: (cont.) 2. Fill in the data table below with the appropriate easureents. Measureents Maxiu velocity Miniu velocity Average velocity Table height Predicted ax. ipact point Predicted in. ipact point Predicted avg. ipact point Actual ipact point distance /s /s /s Calculations: (Show your work.) 1. Find the tie the ball will be in the air. Use the following equation: 1 df y diy viyt a yt 2 2 2. Using your axiu, iniu, and average horizontal velocities, with the following range horizontal velocity t, calculate the predicted axiu, equation: iniu, and average ipact points. Show all three calculations below.
Analysis and Questions: 1. Should you expect any nuerical prediction based on experiental easureents to be exact? Would a range for the prediction be ore appropriate? Explain. 2. Was your actual ipact point between your iniu and axiu ipact predictions? If so, your prediction was successful. 3. You accounted for variations in the velocity easureent in your range prediction. Are there other easureents you used which affect the range prediction? What are they? 4. Did you account for air resistance in your prediction? If so, how? If not, how would air resistance change the distance the ball flies?