Date Course Name Instructor Name Student(s) Name WHERE WILL IT LAND?

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Moses Anthony
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1 Date Course Name Instructor Name Student(s) Name WHERE WILL IT LAND? You have watched a ball roll off a table and strike the floor. What determines where it will land? Could you predict where it will land? In this experiment, you will roll a ball down a ramp and determine the ball s velocity with a pair of Photogates. You will use this information and your knowledge of physics to predict where the ball will land when it hits the floor. You will also find out if you made the right prediction. STUDENT OUTCOMES Through this experiment, students will be able to: - Study the physical quantities involved in projectile motion - Apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectile motion. MATERIALS Tablet PC Computer Laptop Logger Pro Two Vernier Photogates Ramp Carbon Paper Vernier computer interface Metal ball Masking tape Meter stick/ Measuring tape Masking tape PRELIMINARY QUESTIONS. If you were to drop a ball, releasing it from rest, what information would be needed to predict how much time it would take to hit the floor? What assumptions must you make?. If the ball in Question is traveling at a known horizontal velocity when it starts to fall, explain how you would calculate how far it will travel before it hits the ground.

2 . A pair of computer-interfaced Photogates can be used to accurately measure the time interval for an object to break the beam of one Photogate and then another. If you want to know the velocity of the object, what additional information would you need? PROCEDURE and RESULTS. Set up the ramp so that a ball can roll down the ramp, across a short section of the table, and off the table edge. x. Position the Photogates so the ball rolls through each of the Photogates while rolling on the horizontal table. Connect Photogate to DIG/SONIC of the interface and Photogate to the corresponding second port. Photogate should be the first photogate that the ball will go through. To prevent accidental movement of the Photogates, tape them in place.. Mark a starting position ( cm above the table top) and repeatedly release the ball from the same place. Roll the ball down the ramp through each Photogate and off the table. Make sure that the ball does not strike the sides of the Photogates. Reposition the Photogates if necessary.. Open the file 08 Projectile Motion in the Physics with Computers folder. A data table and two graphs are displayed. One graph will show the time 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.. You must enter the distance between the Photogates in order for Logger Pro to calculate the velocity. The program will divide this distance by the time interval it measures to get the velocity (v = s/ t). Carefully measure the distance from the beam of Photogate to the beam of Photogate. (It may be easier to measure from the leading edge of Photogate to the leading edge of Photogate ). To successfully predict the impact point, you must enter an accurate measurement. Enter the distance into Logger Pro by selecting Column Options, then velocity from the Data Menu. In the equation field

3 change the 0. to the actual separation of your gates in meters. Click to complete the edit. 6. Check to see that the Photogates are responding properly by moving your finger through Photogate and then Photogate. The red light on the Photogate should be turning on and off. 7. Roll the ball from the mark on the ramp ( cm above table top), through both Photogates, and catch the ball immediately after it leaves the table. DO NOT let the ball hit the floor during these trials. Repeat five times. Take care not to bump any of the Photogates. Data collection will stop after two minutes. If you need more time, click to restart, choosing Append. After the last trial, click to end data collection. Record the velocity for each trial number in the Data Table. 8. Inspect your velocity data and input these values in the DATA TABLE for the cm release above table top. Did you get the same value every time? 9. Determine the average velocity. Input this value in your Data Table as the horizontal velocity of the ball as it leaves the table top (v ox ). 0. Carefully measure the distance from the table top to the floor and record it as the table height H in the Data Table. Use a plumb bob to locate the point on the floor just beneath the point where the ball will leave the table. Mark this point with tape; this will serve as your floor origin.. Use your velocity value to calculate the distance from the floor origin to the impact point where the ball will hit the floor. You will need to algebraically combine relationships for motion with constant acceleration x = v t + a t 0x y = v t + a t 0y First, simplify the equations above. What is the value of the initial velocity in the vertical direction (v oy )? What is the acceleration in the horizontal direction (a x )? What is the acceleration in the vertical direction (a y )? Remember that the time the ball takes to fall is the same as the time the ball flies horizontally. Use this information and the simplified equations to calculate how far the ball should travel horizontally during the fall. This will be your predicted impact point on the floor. Input this value in the Data Table as the Predicted x.. Place a piece of paper and a carbon paper on top of it at your predicted impact area on the floor. x y

4 . Release the ball from the release point on the ramp and let the ball roll off the table onto the floor. Repeat three times. These should leave marks on the paper.. Measure the distance from the floor origin to the impact point for the three trials and enter the distances (Measured x) in the Data Table. 6. Determine the average value for the Measured x. Input this value in the Data Table. 7. Calculate the standard deviation for the Measured x. Input this in the Data Table 8. Repeat # 7 6 for release points on the ramp of 7 cm, 9 cm, cm and cm above the table top. Record the data in the appropriate Data Table. SHOW YOUR CALCULATIONS. DATA TABLE : CM ABOVE TABLE TOP MEASURED X: TRIAL: AVERAGE

5 DATA TABLE : 7 CM ABOVE TABLE TOP MEASURED X: TRIAL: AVERAGE DATA TABLE : 9 CM ABOVE TABLE TOP MEASURED X: TRIAL: AVERAGE

6 DATA TABLE : CM ABOVE TABLE TOP MEASURED X: TRIAL: AVERAGE DATA TABLE : CM ABOVE TABLE TOP MEASURED X: TRIAL: AVERAGE

7 ANALYSIS. Are the Measured x value exactly equal the Predicted x value in each Data Table? Do you expect the values to be equal? Why or why not?. Do the Predicted x value in each Data Table fall within + σ of the respective average Measured x? If not, what factors influenced the Measured x values?. Draw a graph of Measured x vs V ox. Draw the line that best fits the points and calculate the slope of the graph. What does the slope represent?. Examine the calculations done for the time to fall from the table top to the floor. Is the time affected by the release height above the table top? Explain. QUESTIONS. When the ball rolls off the table top, what quantities affect the Measured x value?. If air resistance was present, how will this affect the Measured x value.. What effect does the force of gravity have on the horizontal velocity of the fall as it falls onto the floor?

Projectile Motion. Photogate 2 Photogate 1 Ramp and Marble. C-clamp. Figure 1

Projectile Motion. Photogate 2 Photogate 1 Ramp and Marble. C-clamp. Figure 1 Projectile Motion Purpose Apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectile motion, and compare the result with direct measurement. Introduction and Theory