You have probably 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 small ball down a ramp and determine the ball’s velocity with a Motion Detector placed near the upper end of the ramp. You will use this information and your knowledge of physics to predict where the ball will land when it hits the floor.
Windows pc, Labpro, Logger pro, Motion Detector, meter stick, ball (1-to-5-cm diameter), plumb bobs ramp, lab jack, carbon paper, tape.
1. Set up the motion track as a ramp inclined to about 10 degrees. Explain in your lab report how you did this. Be sure to sketch your setup, labeling everything. Be sure to include the angle in your lab report data table.
2. Connect the motion detector to DIG 1 of the LabPro. Place the detector at the top of the ramp, which is obtained from an inclined lab track. Position the Motion Detector so the ball rolls down the ramp and away from it.
3. Mark a starting position on the ramp (use a soft pencil and erase it when you have completed the lab) so that you can repeatedly roll the ball from the same place. This is critical. You MUST release the ball from the same position every time. This should be about 0.5 m down the incline from the motion detector. Roll the ball down the ramp 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 measurements! (That would be cheating!)
4. Open the Projectile Motion LoggerPro file in the 4A lab 4 folder. Once you have this graph on the monitor, roll the ball from the ‘mark’ on the ramp. Click . Check to see that the motion detector is responding properly. Make sure your data are not noisy and that the detector is reading the motion at the end of the ramp.
THIS IS THE MOST DIFICULT PART OF THE LAB!!! You must absolutely be sure that you are getting data at the end of the ramp! When you are sure you are getting data at the end of the ramp, determine the instantaneous velocity of the ball when it leaves the ramp. Discuss how your setup went and how confident you are with the motion detector readings.
5. Let the ball roll 10 times to get 10 values of the final velocity. Remember: Do not let the ball hit the floor during these velocity measurements! (That would be cheating!) Include sample graphs produced from LoggerPro of both the position and velocity graphs. Put this data in a table.
6. Inspect your velocity data. Did you get the same value every time? Determine the average, maximum, and minimum values. Calculate the horizontal and vertical components of the velocity for each. Put this data in a table. Discuss the results of your velocity measurements in your lab report.
7. Carefully measure the distance from the launch point on the ramp 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 theramp. Mark this point with tape; it will serve as your floor origin .
8. Use the velocity values and the height to calculate the distance from the floor origin to the impact point where the ball will hit the floor. You will need to first derive an expression for the horizontal distance traveled from the kinematics equations for motion with constant acceleration. This derivation must be explained and included in the theory part of your final lab report. What are your assumptions and knowns? Is the track frictionless? What is the value of the initial velocity in the vertical direction? What is the acceleration in the horizontal direction ( a x
)? What is the acceleration in the vertical direction? Also calculate the time of flight from your data points.

9. To account for the variations you saw in the velocity measurements, repeat the calculation in Step 8 for the minimum and maximum velocity data points. These two additional points show the limits of impact range that you might expect, considering the variation in your velocity measurement. Mark these points on the floor as well. From these values you can determine the uncertainty in your predictions. State your final prediction in standard form; ex: 1.23m +/- .01m.
10 . Mark your predicted impact point on the floor on a piece of white paper. Tape this paper down. Mark the max and min values. Be sure the impact point is along the line of the track.
Place the carbon paper on top of the white paper and tape it down too. Call your instructor over to witness the launch test. Release the ball from the marked starting point, and let the ball roll off the ramp. Check under the carbon paper and see if you hit the target! Was it within your error? Launch the ball at least 5 times to make at least 5 impact marks.
11. Circle each impact mark made by the ball on the target paper. Measure the distance from the center of each circle to the floor origin. Get an average value of the actual distance the ball hits the ground. If you were not successful, try a few more times.
12. If your ball did not fall withing your range of predicted values, check your calculations and try again. You might want to measure the time of flight off the ramp to the ground to check that a derived value for the time matches.
1.
Should you expect any numerical prediction based on experimental measurements to be exact? Why is a range for the prediction more appropriate? Explain. Be sure to express your final prediction in standard form with its uncertainty and range of values.
2.
Was your actual impact point between your minimum and maximum impact predictions? If so, your prediction was successful. What is the percent difference between the predicted and actual value?
3.
You accounted for variations in the velocity measurement in your range prediction. Are there other measurements 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?