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Projectile Motion - Wappingers Central School District

By Yvonne Kelley,2014-03-17 22:43
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Projectile Motion - Wappingers Central School DistrictProjec

    Projectile Motion

    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 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.

     Figure 1

    OBJECTIVES

     Measure the velocity of a ball using two Photogates and computer software for timing.

     Apply concepts from two-dimensional kinematics to predict the impact point of a ball in

    projectile motion.

     Take into account trial-to-trial variations in the velocity measurement when calculating the

    impact point.

MATERIALS

    Power Macintosh or Windows PC plumb bob

    LabPro or Universal Lab Interface ramp

    Logger Pro two ring stands

    two Vernier Photogates two right-angle clamps

    ball (1- to 5-cm diameter) meter stick or metric measuring tape

    masking tape target

PRELIMINARY QUESTIONS

    1. If you were to drop a ball, releasing it from rest, what information would be needed to predict

    how much time it would take for the ball to hit the floor? What assumptions must you make?

    Physics with Computers 8 - 1

    2. If the ball in Question 1 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. 3. 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 wanted to know the

    velocity of the object, what additional information would you need?

    PROCEDURE

    1. Set up a low ramp made of angle molding on a table so that a ball can roll down the ramp,

    across a short section of table, and off the table edge as shown in Figure 1. The end of the

    ramp should be about 50 cm from the edge of the lab bench.

    2. Position the Photogates so the ball rolls through each of the Photogates while rolling on the

    horizontal table surface (but not on the ramp). Approximately center the detection line of each

    Photogate on the middle of the ball. Connect Photogate 1 to the DG 1 of the ULI or

    DIG/SONIC 1 of the LabPro and Photogate 2 to the corresponding second port. The two

    photogates should be parallel to one another

    3. Mark a starting position on the ramp so that you can repeatedly roll the ball from the same

    place. You may want to start from the very end of the ramp. Roll the ball down the ramp

    through each Photogate and off the table. Catch the ball as soon as it leaves the table. Mark

    the point where the ball leaves the table. Note: Do not let the ball hit the floor during

    these trials or during the following velocity measurements. Make sure that the ball does

    not strike the sides of the Photogates. Reposition the Photogates if necessary. 4. Open the file in the 08 Projectile Motion in the folder 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.

    5. You must enter the distance, d, between 8 to 12 cm Photogates in order for Logger Pro to calculate the

    velocity. The program will divide this distance by the

    time interval t it measures to get the velocity (v =

    d/t). Carefully measure the distance from the

    beam of Photogate 1 to the beam of Photogate 2. (It

    may be easier to measure from the leading edge of

    Photogate 1 to the leading edge of Photogate 2.) To

    Photogate 2 Photogate 1 successfully predict the impact point, you must

    enter an accurate measurement. Enter the distance Figure 2 into Logger Pro by selecting Data Collection from

    the Setup menu, then clicking the Sampling tab.

    Change the number in the Distance Between Gates field to the correct distance in meters.

    Click You may also use the scroll bar or double click on the “Gate Spacing” section .

    to enter your information.

    6. Click. Check to see that the Photogates are responding properly by moving your

    finger through Photogate 1 and then Photogate 2. Logger Pro will plot a time interval (t)

    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 from the mark on the ramp, through both Photogates, and catch the ball

    immediately after it leaves the table. Repeat nine times. Take care not to bump any of the

    Photogates, or your velocity data will not be precise. 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. Did you get the same value every time? Determine the average, maximum, and minimum values by clicking once on the velocity vs. time graph and then

    clicking the Statistics button,. What one value would be most representative of all ten

    measurements?

    9. 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; it will serve as your floor

    origin.

    plumb bob

    floor origin

     Figure 3

     10. 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 21?;;xvtatix2 21?;;yvtatiy2

    First, simplify the equations above. What is the value of the initial velocity in the vertical direction (v)? What is the acceleration in the horizontal direction (a)? What is the iyx

    acceleration in the vertical direction (a)? Remember that the time the ball takes to fall is the y

    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. Note: you need to show

    all your work for the calculations of time and horizontal distance in the space below.

    Mark your predicted impact point on the floor with tape and position a target at the predicted impact point. Be sure the impact point is along the line of the track.

     11. To account for the variations you saw in the Photogate velocity measurements, repeat the calculation in Step 10 for the minimum and maximum velocity. 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 your target sheet as well.

     12. After your instructor gives you permission, release the ball from the marked starting point,

    and let the ball roll off the table and onto the floor. Mark the point of impact with tape.

    Measure the distance from the floor origin to the actual impact and enter the distance in the

    data table.

    DATA TABLE

    Trial Velocity

     (m/s)

    1 Maximum velocity m/s

    2 Minimum velocity m/s

    3 Average velocity m/s

    4 Table height m

    5 Predicted impact point m

    6 Minimum impact point distance m

    7 Maximum impact point distance m

    8 Actual impact point distance m

    9

    10

ANALYSIS

    1. Should you expect any numerical prediction based on experimental measurements to be exact?

    Would a range for the prediction be more appropriate? Explain.

    2. Was your actual impact point between your minimum and maximum impact predictions? If so,

    your prediction was successful.

    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?

    ERROR ANALYSIS & CONCLUSIONS

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